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Journal articles on the topic 'Fibres de Springer'

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Published: 8 June 2024

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1

Kottwitz, Robert, and Eva Viehmann. "Generalized affine Springer fibres." Journal of the Institute of Mathematics of Jussieu 11, no. 3 (January 3, 2012): 569–609. http://dx.doi.org/10.1017/s147474801100020x.

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AbstractThis paper studies two new kinds of affine Springer fibres that are adapted to the root valuation strata of Goresky–Kottwitz–MacPherson. In addition it develops various linear versions of Katz's Hodge–Newton decomposition.

2

SCHÄFER, GISA. "A GRAPHICAL CALCULUS FOR 2-BLOCK SPALTENSTEIN VARIETIES." Glasgow Mathematical Journal 54, no. 2 (March 29, 2012): 449–77. http://dx.doi.org/10.1017/s0017089512000110.

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AbstractWe generalise statements known about Springer fibres associated to nilpotents with two Jordan blocks to Spaltenstein varieties. We study the geometry of generalised irreducible components (i.e. Bialynicki-Birula cells) and their pairwise intersections. In particular, we develop a graphical calculus that encodes their structure as iterated fibre bundles with ℂℙ1 as base spaces, and compute their cohomology. At the end, we present a connection with coloured cobordisms generalising the construction of Khovanov (M. Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101(3) (2000), 359–426) and Stroppel (C. Stroppel, Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology, Compositio Mathematica145(4) (2009), 954–992).

3

Nandakumar, V., D. Rosso, and N. Saunders. "Irreducible components of exotic Springer fibres." Journal of the London Mathematical Society 98, no. 3 (July 16, 2018): 609–37. http://dx.doi.org/10.1112/jlms.12152.

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4

Chen, Zongbin. "Pureté des fibres de Springer affines pour $GL_4$." Bulletin de la Société mathématique de France 142, no. 2 (2014): 193–222. http://dx.doi.org/10.24033/bsmf.2663.

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5

Chaudouard, Pierre-Henri, and Gérard Laumon. "Sur l'homologie des fibres de Springer affines tronquées." Duke Mathematical Journal 145, no. 3 (December 2008): 443–535. http://dx.doi.org/10.1215/00127094-2008-057.

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6

BOUTHIER, ALEXIS. "DIMENSION DES FIBRES DE SPRINGER AFFINES POUR LES GROUPES." Transformation Groups 20, no. 3 (July 30, 2015): 615–63. http://dx.doi.org/10.1007/s00031-015-9326-9.

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7

Fresse, Lucas. "Nombres de Betti des fibres de Springer de type A." Comptes Rendus Mathematique 347, no. 5-6 (March 2009): 283–87. http://dx.doi.org/10.1016/j.crma.2009.01.014.

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8

Jóźwicki, Mateusz Łukasz, Mateusz Gargol, Małgorzata Gil-Kowalczyk, and Paweł Mergo. "Commercially available granulates PMMA and PS - potential problems with the production of polymer optical fibers." Photonics Letters of Poland 12, no. 3 (September 30, 2020): 79. http://dx.doi.org/10.4302/plp.v12i3.1036.

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The aim of the study was to verify the usefulness of commercially available granulates of PMMA (poly (methyl methacrylate) and PS (polystyrene) for the production of polymer optical fibers by extrusion method. Samples were subjected to thermal processing in various conditions (different temperatures and exposure time). Thermal (TG/DTG) and spectroscopic (ATR/FT-IR) analyses were carried out to analyze changes in the samples. Based on FT-IR analysis of liquid monomers and granulates the conversion of double bonds was calculated, which gave us a picture of the degree of monomers conversion, crucial information from the technological point of view. Full Text: PDF ReferencesO. Ziemann, J. Krauser, P.E. Zamzow, W. Daum, POF Polymer Optical Fibersfor Data Communication (Berlin: Springer 2008). DirectLink P. Stajanca et al. "Solution-mediated cladding doping of commercial polymer optical fibers", Opt. Fiber Technol. 41, 227-234, (2018). CrossRef K. Peters, "Polymer optical fiber sensors—a review", Smart Mater. Struct., 20 013002 (2011) CrossRef J. Zubia and J. Arrue, "Plastic Optical Fibers: An Introduction to Their Technological Processes and Applications", Opt. Fiber Technol. 7 ,101-40 (2001) CrossRef M. Beckers, T. Schlüter, T. Gries, G. Seide, C.-A. Bunge, "6 - Fabrication techniques for polymer optical fibres", Polymer Optical Fibres, 187-199 (2017) CrossRef M. Niedźwiedź , M. Gil, M. Gargol , W. Podkościelny, P. Mergo, "Determination of the optimal extrusion temperature of the PMMA optical fibers", Phot. Lett. Poland 11, 7-9 (2019) CrossRef

9

Ehrig, Michael, and Catharina Stroppel. "2-row Springer Fibres and Khovanov Diagram Algebras for Type D." Canadian Journal of Mathematics 68, no. 6 (December 1, 2016): 1285–333. http://dx.doi.org/10.4153/cjm-2015-051-4.

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AbstractWe study in detail two row Springer fibres of even orthogonal type from an algebraic as well as a topological point of view. We show that the irreducible components and their pairwise intersections are iterated ℙ1-bundles. Using results of Kumar and Procesi we compute the cohomology ring with its action of the Weyl group. The main tool is a type D diagram calculus labelling the irreducible components in a convenient way that relates to a diagrammatical algebra describing the category of perverse sheaves on isotropic Grassmannians based on work of Braden. The diagram calculus generalizes Khovanov's arc algebra to the type D setting and should be seen as setting the framework for generalizing well-known connections of these algebras in type A to other types.

10

BOUTHIER, ALEXIS, and JINGREN CHI. "Correction to: DIMENSION DES FIBRES DE SPRINGER AFFINES POUR LES GROUPES." Transformation Groups 23, no. 4 (October 15, 2018): 1217–22. http://dx.doi.org/10.1007/s00031-018-9496-3.

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11

Fresse, Lucas. "Composantes singulières des fibres de Springer dans le cas deux-colonnes." Comptes Rendus Mathematique 347, no. 11-12 (June 2009): 631–36. http://dx.doi.org/10.1016/j.crma.2009.04.005.

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12

Nandakumar, Vinoth, Daniele Rosso, and Neil Saunders. "Irreducible components of exotic Springer fibres II : The exotic Robinson–Schensted algorithm." Pacific Journal of Mathematics 310, no. 2 (March 8, 2021): 447–85. http://dx.doi.org/10.2140/pjm.2021.310.447.

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13

Stroppel, Catharina. "Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology." Compositio Mathematica 145, no. 4 (July 2009): 954–92. http://dx.doi.org/10.1112/s0010437x09004035.

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AbstractFor a fixed parabolic subalgebra 𝔭 of $\mathfrak {gl}(n,\mathbb {C})$ we prove that the centre of the principal block 𝒪0𝔭 of the parabolic category 𝒪 is naturally isomorphic to the cohomology ring H*(ℬ𝔭) of the corresponding Springer fibre. We give a diagrammatic description of 𝒪0𝔭 for maximal parabolic 𝔭 and give an explicit isomorphism to Braden’s description of the category PervB(G(k,n)) of Schubert-constructible perverse sheaves on Grassmannians. As a consequence Khovanov’s algebra ℋn is realised as the endomorphism ring of some object from PervB(G(n,n)) which corresponds under localisation and the Riemann–Hilbert correspondence to a full projective–injective module in the corresponding category 𝒪0𝔭. From there one can deduce that Khovanov’s tangle invariants are obtained from the more general functorial invariants in [C. Stroppel, Categorification of the Temperley Lieb category, tangles, and cobordisms via projective functors, Duke Math. J. 126(3) (2005), 547–596] by restriction.

14

Henderson, Anthony. "Exterior powers of the reflection representation in the cohomology of Springer fibres." Comptes Rendus Mathematique 348, no. 19-20 (October 2010): 1055–58. http://dx.doi.org/10.1016/j.crma.2010.09.015.

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15

Niedźwiedź, Malwina Julita, Małgorzata Gil, Mateusz Gargol, Wiesław Marian Podkościelny, and Paweł Mergo. "Determination of the optimal extrusion temperature of the PMMA optical fibers." Photonics Letters of Poland 11, no. 1 (April 3, 2019): 7. http://dx.doi.org/10.4302/plp.v11i1.889.

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The aim of this work was to determine optimal extrusion temperature for polymer optical fibers. For preliminary studies poly(methyl methacrylate) (PMMA) granulate was used. Samples of commercially available PMMA were subjected to four different temperatures in which were kept in oven for three different period of time. To examine the changes in the chemical structure of the polymer, an ATR-FT-IR (Attenuation Total Reflection Fourier Transform Infrared Spectroscopy) was chosen. Full Text: PDF ReferencesK. Peters, "Polymer optical fiber sensors—a review", Smart Mater. Struct. 20, 013002 (2011) CrossRef O. Ziemann, J. Krauser, P.E. Zamzow, W. Daum, "POF Polymer Optical Fibers for Data Communication" (New York, Springer-Verlag Berlin Heidelberg 2002). CrossRef M.A. van Eijkelenborg, M.C.J. Large, A. Argyros, J. Zagari, S. Manos, N.A. Issa, I. Bassett, S. Fleming, R.C. McPhedran, C. Martijn de Sterke, N.A.P. Nicorovici, "Microstructured polymer optical fibre", Opt Express 9, 319 (2001). CrossRef O. Çetinkaya, G. Wojcik, P. Mergo, "Decreasing diameter fluctuation of polymer optical fiber with optimized drawing conditions", Mater Res Express 5, 1 (2018). CrossRef P. Mergo, M. Gil, K. Skorupski, J. Klimek, G. Wójcik, J. Pędzisz, J. Kopec, K. Poruraj, L. Czyzewska, A. Walewski, A. Gorgol, "Low loss poly(methyl methacrylate) useful in polymer optical fibres technology", Phot. Lett. Poland, 5, 170 (2013). CrossRef J. Grdadolnik, "ATR-FTIR Spectroscopy: Its advantages and limitations", Acta Chim Slov. 49, 631 (2002). DirectLink P. Borowski, S. Pasieczna-Patkowska, M. Barczak, K. Pilorz, "Theoretical Determination of the Infrared Spectra of Amorphous Polymers", J Phys Chem A 116, 7424 (2012). CrossRef G. Socrates, "Infrared and Raman Characteristic Group Frequencies Tables and Charts" Third Edition (Baffins Lane Chichester, John Wiley & Sons Ltd 2001). DirectLink W. Schnabel, Polymer Degradation Principles and Practical Applications (Berlin, Akademie-Verlag 1981). DirectLink

16

Manley, T. R. "Carbon fibres and their composites. Edited by E. Fitzer, Springer-Verlag, Berlin, 1985. pp. 296, price DM 128.00. ISBN 3-540-15804-9." British Polymer Journal 18, no. 5 (September 1986): 349–50. http://dx.doi.org/10.1002/pi.4980180515.

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17

Woliński, Tomasz, Sławomir Ertman, Katarzyna Rutkowska, Daniel Budaszewski, Marzena Sala-Tefelska, Miłosz Chychłowski, Kamil Orzechowski, Karolina Bednarska, and Piotr Lesiak. "Photonic Liquid Crystal Fibers – 15 years of research activities at Warsaw University of Technology." Photonics Letters of Poland 11, no. 2 (July 1, 2019): 22. http://dx.doi.org/10.4302/plp.v11i2.907.

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Research activities in the area of photonic liquid crystal fibers carried out over the last 15 years at Warsaw University of Technology (WUT) have been reviewed and current research directions that include metallic nanoparticles doping to enhance electro-optical properties of the photonic liquid crystal fibers are presented. Full Text: PDF ReferencesT.R. Woliński et al., "Propagation effects in a photonic crystal fiber filled with a low-birefringence liquid crystal", Proc. SPIE, 5518, 232-237 (2004). CrossRef F. Du, Y-Q. Lu, S.-T. Wu, "Electrically tunable liquid-crystal photonic crystal fiber", Appl. Phys. Lett. 85, 2181-2183 (2004). CrossRef T.T. Larsen, A. Bjraklev, D.S. Hermann, J. Broeng, "Optical devices based on liquid crystal photonic bandgap fibres", Opt. Express, 11, 20, 2589-2596 (2003). CrossRef T.R. Woliński et al., "Tunable properties of light propagation in photonic liquid crystal fibers", Opto-Electron. Rev. 13, 2, 59-64 (2005). CrossRef M. Chychłowski, S. Ertman, T.R. Woliński, "Splay orientation in a capillary", Phot. Lett. Pol. 2, 1, 31-33 (2010). CrossRef T.R. Woliński et al., "Photonic liquid crystal fibers — a new challenge for fiber optics and liquid crystals photonics", Opto-Electron. Rev. 14, 4, 329-334 (2006). CrossRef T.R. Woliński et al., "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres", Meas. Sci. Technol. 17, 985-991 (2006). CrossRef T.R. Woliński et al., "Photonic Liquid Crystal Fibers for Sensing Applications", IEEE Trans. Inst. Meas. 57, 8, 1796-1802 (2008). CrossRef T.R. Woliński, et al., "Multi-Parameter Sensing Based on Photonic Liquid Crystal Fibers", Mol. Cryst. Liq. Cryst. 502: 220-234., (2009). CrossRef T.R. Woliński, Xiao G and Bock WJ Photonics sensing: principle and applications for safety and security monitoring, (New Jersey, Wiley, 147-181, 2012). CrossRef T.R. Woliński et al., "Propagation effects in a polymer-based photonic liquid crystal fiber", Appl. Phys. A 115, 2, 569-574 (2014). CrossRef S. Ertman et al., "Optofluidic Photonic Crystal Fiber-Based Sensors", J. Lightwave Technol., 35, 16, 3399-3405 (2017). CrossRef S. Ertman et al., "Recent Progress in Liquid-Crystal Optical Fibers and Their Applications in Photonics", J. Lightwave Technol., 37, 11, 2516-2526 (2019). CrossRef M.M. Tefelska et al., "Electric Field Sensing With Photonic Liquid Crystal Fibers Based on Micro-Electrodes Systems", J. Lightwave Technol., 33, 2, 2405-2411, (2015). CrossRef S. Ertman et al., "Index Guiding Photonic Liquid Crystal Fibers for Practical Applications", J. Lightwave Technol., 30, 8, 1208-1214 (2012). CrossRef K. Mileńko, S. Ertman, T. R. Woliński, "Numerical analysis of birefringence tuning in high index microstructured fiber selectively filled with liquid crystal", Proc. SPIE - The International Society for Optical Engineering, 8794 (2013). CrossRef O. Jaworska and S. Ertman, "Photonic bandgaps in selectively filled photonic crystal fibers", Phot. Lett. Pol., 9, 3, 79-81 (2017). CrossRef I.C. Khoo, S.T.Wu, "Optics and Nonlinear Optics of Liquid Crystals", World Scientific (1993). CrossRef P. Lesiak et al., "Thermal optical nonlinearity in photonic crystal fibers filled with nematic liquid crystals doped with gold nanoparticles", Proc. SPIE 10228, 102280N (2017). CrossRef K. Rutkowska, T. Woliński, "Modeling of light propagation in photonic liquid crystal fibers", Photon. Lett. Poland 2, 3, 107 (2010). CrossRef K. Rutkowska, L-W. Wei, "Assessment on the applicability of finite difference methods to model light propagation in photonic liquid crystal fibers", Photon. Lett. Poland 4, 4, 161 (2012). CrossRef K. Rutkowska, U. Laudyn, P. Jung, "Nonlinear discrete light propagation in photonic liquid crystal fibers", Photon. Lett. Poland 5, 1, 17 (2013). CrossRef M. Murek, K. Rutkowska, "Two laser beams interaction in photonic crystal fibers infiltrated with highly nonlinear materials", Photon. Lett. Poland 6, 2, 74 (2014). CrossRef M.M. Tefelska et al., "Photonic Band Gap Fibers with Novel Chiral Nematic and Low-Birefringence Nematic Liquid Crystals", Mol. Cryst. Liq. Cryst., 558, 184-193, (2012). CrossRef M.M. Tefelska et al., "Propagation Effects in Photonic Liquid Crystal Fibers with a Complex Structure", Acta Phys. Pol. A, 118, 1259-1261 (2010). CrossRef K. Orzechowski et al., "Polarization properties of cubic blue phases of a cholesteric liquid crystal", Opt. Mater. 69, 259-264 (2017). CrossRef H. Yoshida et al., "Heavy meson spectroscopy under strong magnetic field", Phys. Rev. E 94, 042703 (2016). CrossRef J. Yan et al., "Extended Kerr effect of polymer-stabilized blue-phase liquid crystals", Appl. Phys. Lett. 96, 071105 (2010). CrossRef C.-W. Chen et al., "Random lasing in blue phase liquid crystals", Opt. Express 20, 23978-23984 (2012). CrossRef C.-H. Lee et al., "Polarization-independent bistable light valve in blue phase liquid crystal filled photonic crystal fiber", Appl. Opt. 52, 4849-4853 (2013). CrossRef D. Poudereux et al., "Infiltration of a photonic crystal fiber with cholesteric liquid crystal and blue phase", Proc. SPIE 9290 (2014). CrossRef K. Orzechowski et al., "Optical properties of cubic blue phase liquid crystal in photonic microstructures", Opt. Express 27, 10, 14270-14282 (2019). CrossRef M. Wahle, J. Ebel, D. Wilkes, H.S. Kitzerow, "Asymmetric band gap shift in electrically addressed blue phase photonic crystal fibers", Opt. Express 24, 20, 22718-22729 (2016). CrossRef K. Orzechowski et al., "Investigation of the Kerr effect in a blue phase liquid crystal using a wedge-cell technique", Phot. Lett. Pol. 9, 2, 54-56 (2017). CrossRef M.M. Sala-Tefelska et al., "Influence of cylindrical geometry and alignment layers on the growth process and selective reflection of blue phase domains", Opt. Mater. 75, 211-215 (2018). CrossRef M.M. Sala-Tefelska et al., "The influence of orienting layers on blue phase liquid crystals in rectangular geometries", Phot. Lett. Pol. 10, 4, 100-102 (2018). CrossRef P. G. de Gennes JP. The Physics of Liquid Crystals. (Oxford University Press 1995). CrossRef L.M. Blinov and V.G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials (New York, NY: Springer New York 1994). CrossRef D. Budaszewski, A.J. Srivastava, V.G. Chigrinov, T.R. Woliński, "Electro-optical properties of photo-aligned photonic ferroelectric liquid crystal fibres", Liq. Cryst., 46 2, 272-280 (2019). CrossRef V. G. Chigrinov, V. M. Kozenkov, H-S. Kwok. Photoalignment of Liquid Crystalline Materials (Chichester, UK: John Wiley & Sons, Ltd 2008). CrossRef M. Schadt et al., "Surface-Induced Parallel Alignment of Liquid Crystals by Linearly Polymerized Photopolymers", Jpn. J. Appl. Phys.31, 2155-2164 (1992). CrossRef D. Budaszewski et al., "Photo-aligned ferroelectric liquid crystals in microchannels", Opt. Lett. 39, 4679 (2014). CrossRef D. Budaszewski, et al., "Photo‐aligned photonic ferroelectric liquid crystal fibers", J. Soc. Inf. Disp. 23, 196-201 (2015). CrossRef O. Stamatoiu, J. Mirzaei, X. Feng, T. Hegmann, "Nanoparticles in Liquid Crystals and Liquid Crystalline Nanoparticles", Top Curr Chem 318, 331-392 (2012). CrossRef A. Siarkowska et al., "Titanium nanoparticles doping of 5CB infiltrated microstructured optical fibers", Photonics Lett. Pol. 8 1, 29-31 (2016). CrossRef A. Siarkowska et al., "Thermo- and electro-optical properties of photonic liquid crystal fibers doped with gold nanoparticles", Beilstein J. Nanotechnol. 8, 2790-2801 (2017). CrossRef D. Budaszewski et al., "Nanoparticles-enhanced photonic liquid crystal fibers", J. Mol. Liq. 267, 271-278 (2018). CrossRef D. Budaszewski et al., "Enhanced efficiency of electric field tunability in photonic liquid crystal fibers doped with gold nanoparticles", Opt. Exp. 27, 10, 14260-14269 (2019). CrossRef

18

Precup, Martha, and Edward Richmond. "An equivariant basis for the cohomology of Springer fibers." Transactions of the American Mathematical Society, Series B 8, no. 17 (June 10, 2021): 481–509. http://dx.doi.org/10.1090/btran/57.

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Springer fibers are subvarieties of the flag variety that play an important role in combinatorics and geometric representation theory. In this paper, we analyze the equivariant cohomology of Springer fibers for G L n ( C ) GL_n(\mathbb {C}) using results of Kumar and Procesi that describe this equivariant cohomology as a quotient ring. We define a basis for the equivariant cohomology of a Springer fiber, generalizing a monomial basis of the ordinary cohomology defined by De Concini and Procesi and studied by Garsia and Procesi. Our construction yields a combinatorial framework with which to study the equivariant and ordinary cohomology rings of Springer fibers. As an application, we identify an explicit collection of (equivariant) Schubert classes whose images in the (equivariant) cohomology ring of a given Springer fiber form a basis.

19

Cimek, Jarosław, Xavier Forestier, Ryszard Stepien, Mariusz Klimczak, and Ryszard Buczynski. "Synthesis conditions of ZBLAN glass for mid-infrared optical components." Photonics Letters of Poland 10, no. 1 (March 31, 2018): 8. http://dx.doi.org/10.4302/plp.v10i1.804.

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We report on successful synthesis of ZBLAN glass. Different purity of zirconium tetrafluoride used for synthesis and fluorinating agents were analyzed to obtain high optical quality glass. Among fluorinating agents we used ammonium bifluoride, xenon difluoride and sulfur hexafluoride. The best results in form of synthetized glasses have transmission window extending from 0.2 to 8.0 um, which allows to fabricate fibers for mid-infrared applications. Full Text: PDF ReferencesR. Stępień, J. Cimek, D. Pysz, I. Kujawa, M. Klimczak, and R. Buczyński, Soft glasses for photonic crystal fibers and microstructured optical components, Opt. Eng. 53, 071815 (2014). CrossRef D. Pysz, I. Kujawa, R. Stępień, M. Klimczak, A. Filipkowski, M. Franczyk, L. Kociszewski, J. Buźniak, K. Haraśny, R. Buczyński, Stack and draw fabrication of soft glass microstructured fiber optics, Bull. Pol. Acad. Sci.-Tech. Sci., 62(4), 667-683 (2014). CrossRef R. Kasztelanic, I. Kujawa, R. Stępień, K. Haraśny, D. Pysz and R. Buczyński, Molding of soft glass refraction mini lens with hot embossing process for broadband infrared transmission systems, Infrared Phys. Technol. 61, 299-305 (2013). CrossRef Moynihan C.T. (1987) Crystallization Behavior of Fluorozirconate Glasses. In: Almeida R.M. (eds) Halide Glasses for Infrared Fiberoptics. NATO ASI Series (Series E: Applied Sciences), 123, Springer, Dordrecht. CrossRef M. R. Majewski, R. I. Woodward, S. D. Jackson, Dysprosium-doped ZBLAN fiber laser tunable from 2.8?m to 3.4?m, pumped at 1.7?m, Opt. Lett. 43, 971-974 (2018). CrossRef G Bharathan, R. I. Woodward, M. Ams, D. D. Hudson, S. D. Jackson, A. Fuerbach, Direct inscription of Bragg gratings into coated fluoride fibers for widely tunable and robust mid-infrared lasers, Opt. Express 25, 30013-30019 (2017). CrossRef Y. Shen, Y. Wang, H. Chen, K. Luan, M. Tao, J. Si, Wavelength-tunable passively mode-locked mid-infrared Er3+-doped ZBLAN fiber laser, Sci. Rep. 7, 14913 (2017). CrossRef J. Méndez-Ramos, P. Acosta-Mora, J. C. Ruiz-Morales, T. Hernández, M. E. Borges, P. Esparza, Heavy rare-earth-doped ZBLAN glasses for UV?blue up-conversion and white light generation, J. Lumin. 143, 479-483 (2013). CrossRef X. Jiang, N. Y. Joly, M. A. Finger, F. Babic, G. K. L. Wong, J. C. Travers, P. St. J. Russell, Deep-ultraviolet to mid-infrared supercontinuum generated in solid-core ZBLAN photonic crystal fibre, Nat. Photonics 9, 133?139 (2015). CrossRef X. Jiang, N. Y. Joly, M. A. Finger, F. Babic, M. Pang, R. Sopalla, M. H. Frosz, S. Poulain, M. Poulain, V. Cardin, J. C. Travers, P. St. J. Russell, Supercontinuum generation in ZBLAN glass photonic crystal fiber with six nanobore cores, Opt. Lett. 41, 4245-4248 (2016). CrossRef A. Medjouri, E. B. Meraghni, H. Hathroubi, D. Abed, L. M. Simohamed, O. Ziane, Design of ZBLAN photonic crystal fiber with nearly zero ultra-flattened chromatic dispersion for supercontinuum generation, Optik 135, 417?425 (2017). CrossRef D. C. Tee, N. Tamchek, C. H. Raymond Ooi, Numerical Modeling of the Fundamental Characteristics of ZBLAN Photonic Crystal Fiber for Communication in 2?3 ?m Midinfrared Region, IEEE Photon. J. 8, 4500713 (2016) . CrossRef Y. Dai, K. Takahashi, I. Yamaguchi, Thermal oxidation of fluorozirconate glass and fibres, J. Mater. Sci. Lett. 12, 1648?1651 (1993). CrossRef P. Hlubina, White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica, Opt. Commun. 193, 1-7 (2001). CrossRef F. Gan, Optical properties of fluoride glasses: a review, J. Non Cryst. Sol. 184, 9-20 (1995). CrossRef A. Filipkowski, B. Piechal, D. Pysz, R. Stepien, A. Waddie, M. R. Taghizadeh, and R. Buczynski, Nanostructured gradient index micro axicons made by a modified stack and draw method, Opt. Lett. 40, 5200-5203 (2015). CrossRef R. Kasztelanic, A. Filipkowski, D. Pysz, R. Stepień, A. J. Waddie, M. R. Taghizadeh, and R. Buczynski, High resolution Shack-Hartmann sensor based on array of nanostructured GRIN lenses, Opt. Express 25, 1680-1691 (2017). CrossRef

20

Olasupo Jon, Felemu. "Springer Fibers of Hook Type and Schubert Points." International Journal of Science and Research (IJSR) 12, no. 2 (February 5, 2023): 377–85. http://dx.doi.org/10.21275/sr23203080130.

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21

KIM, D. "EULER CHARACTERISTIC OF SPRINGER FIBERS." Transformation Groups 24, no. 2 (August 11, 2018): 403–28. http://dx.doi.org/10.1007/s00031-018-9487-4.

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22

Graham, William, and R. Zierau. "Smooth components of Springer fibers." Annales de l’institut Fourier 61, no. 5 (2011): 2139–82. http://dx.doi.org/10.5802/aif.2669.

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23

Tsai, Cheng-Chiang. "Components of Affine Springer Fibers." International Mathematics Research Notices 2020, no. 6 (May 9, 2018): 1882–919. http://dx.doi.org/10.1093/imrn/rny085.

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Abstract Let G be a connected split reductive group over a field of characteristic zero or sufficiently large characteristic, $\gamma _0\in (\operatorname{Lie}\mathbf{G})((t))$ be any topologically nilpotent regular semisimple element, and $\gamma =t\gamma _0$. Using methods from p-adic orbital integrals, we show that the number of components of the Iwahori affine Springer fiber over $\gamma$ modulo $Z_{\mathbf{G}((t))}(\gamma )$ is equal to the order of the Weyl group.

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Precup, Martha, and Julianna Tymoczko. "Springer fibers and Schubert points." European Journal of Combinatorics 76 (February 2019): 10–26. http://dx.doi.org/10.1016/j.ejc.2018.08.010.

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Goresky, Mark, Robert Kottwitz, and Robert MacPherson. "Regular points in affine Springer fibers." Michigan Mathematical Journal 53, no. 1 (April 2005): 97–107. http://dx.doi.org/10.1307/mmj/1114021087.

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Goresky, Mark, Robert Kottwitz, and Robert MacPherson. "Purity of equivalued affine Springer fibers." Representation Theory of the American Mathematical Society 10, no. 6 (February 20, 2006): 130–46. http://dx.doi.org/10.1090/s1088-4165-06-00200-7.

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Leidwanger, Séverine, and Nicolas Perrin. "Study of some orthosymplectic Springer fibers." Journal of Algebra 335, no. 1 (June 2011): 83–95. http://dx.doi.org/10.1016/j.jalgebra.2011.03.011.

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Nadler, David. "Springer theory via the Hitchin fibration." Compositio Mathematica 147, no. 5 (July 29, 2011): 1635–70. http://dx.doi.org/10.1112/s0010437x1100546x.

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Abstract:

AbstractWe develop the Springer theory of Weyl group representations in the language of symplectic topology. Given a semisimple complex group G, we describe a Lagrangian brane in the cotangent bundle of the adjoint quotient 𝔤/G that produces the perverse sheaves of Springer theory. The main technical tool is an analysis of the Fourier transform for constructible sheaves from the perspective of the Fukaya category. Our results can be viewed as a toy model of the quantization of Hitchin fibers in the geometric Langlands program.

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Yun, Zhiwei. "Langlands duality and global Springer theory." Compositio Mathematica 148, no. 3 (March 19, 2012): 835–67. http://dx.doi.org/10.1112/s0010437x11007433.

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Abstract:

AbstractWe compare the cohomology of (parabolic) Hitchin fibers for Langlands dual groups G and G∨. The comparison theorem fits in the framework of the global Springer theory developed by the author. We prove that the stable parts of the parabolic Hitchin complexes for Langlands dual group are naturally isomorphic after passing to the associated graded of the perverse filtration. Moreover, this isomorphism intertwines the global Springer action on one hand and Chern class action on the other. Our result is inspired by the mirror symmetric viewpoint of geometric Langlands duality. Compared to the pioneer work in this subject by T. Hausel and M. Thaddeus, R. Donagi and T. Pantev, and N. Hitchin, our result is valid for more general singular fibers. The proof relies on a variant of Ngô’s support theorem, which is a key point in the proof of the Fundamental Lemma.

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Pagnon, N. G. J., and N. Ressayre. "Adjacency of Young tableaux and the Springer fibers." Selecta Mathematica 12, no. 3-4 (March 13, 2007): 517–40. http://dx.doi.org/10.1007/s00029-006-0027-z.

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Samples, Brandon. "Components of Springer fibers for the exceptional groupsG2andF4." Journal of Algebra 400 (February 2014): 219–48. http://dx.doi.org/10.1016/j.jalgebra.2013.11.014.

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Chen, Zongbin. "On the fundamental domain of affine Springer fibers." Mathematische Zeitschrift 286, no. 3-4 (November 19, 2016): 1323–56. http://dx.doi.org/10.1007/s00209-016-1803-x.

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Fresse, Lucas. "Betti numbers of Springer fibers in type A." Journal of Algebra 322, no. 7 (October 2009): 2566–79. http://dx.doi.org/10.1016/j.jalgebra.2009.07.008.

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Stroppel, Catharina, and Arik Wilbert. "Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory." Mathematische Zeitschrift 292, no. 3-4 (October 17, 2018): 1387–430. http://dx.doi.org/10.1007/s00209-018-2161-7.

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Can, Mahir Bilen, Roger Howe, and Michael Joyce. "An analogue of Springer fibers in certain wonderful compactifications." Journal of Algebra and Its Applications 16, no. 09 (September 30, 2016): 1750172. http://dx.doi.org/10.1142/s0219498817501729.

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Abstract:

We investigate the topological structure of a cellular decomposition of the fixed locus of a unipotent operator of regular Jordan type acting on the wonderful compactification of the variety of complete quadrics and the variety of complete skew forms. The Poincaré polynomial is computed in each case and the poset of cell closures under inclusion is described in the complete quadrics case.

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Fresse, Lucas, Anna Melnikov, and Sammar Sakas-Obeid. "On the structure of smooth components of Springer fibers." Proceedings of the American Mathematical Society 143, no. 6 (January 14, 2015): 2301–15. http://dx.doi.org/10.1090/s0002-9939-2015-12460-4.

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MacPherson, Robert, Robert Kottwitz, and Mark Goresky. "Homology of affine Springer fibers in the unramified case." Duke Mathematical Journal 121, no. 3 (February 2004): 509–61. http://dx.doi.org/10.1215/s0012-7094-04-12135-9.

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Griffin, Sean T., Jake Levinson, and Alexander Woo. "Springer fibers and the Delta Conjecture at t = 0." Advances in Mathematics 439 (March 2024): 109491. http://dx.doi.org/10.1016/j.aim.2024.109491.

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Fresse, Lucas. "Singular components of Springer fibers in the two-column case." Annales de l’institut Fourier 59, no. 6 (2009): 2429–44. http://dx.doi.org/10.5802/aif.2495.

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Fresse, Lucas. "On the singular locus of certain subvarieties of Springer fibers." Mathematical Research Letters 19, no. 4 (2012): 753–66. http://dx.doi.org/10.4310/mrl.2012.v19.n4.a2.

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Pagnon, N. G. J. "Generic fibers of the generalized Springer resolution of type A." Advances in Mathematics 194, no. 2 (July 2005): 437–62. http://dx.doi.org/10.1016/j.aim.2004.07.002.

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Franczyk, Marcin, Dariusz Pysz, Filip Włodarczyk, Ireneusz Kujawa, and Ryszard Buczyński. "Yb3+ doped single-mode silica fibre laser system for high peak power applications." Photonics Letters of Poland 12, no. 4 (December 31, 2020): 118. http://dx.doi.org/10.4302/plp.v12i4.1075.

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Abstract:

We present ytterbium doped silica single-mode fibre components for high power and high energy laser applications. We developed in-house the fibre laser with high efficiency of 65% according to the launched power, the threshold of 1.16W and the fibre length of 20 m. We also elaborated the fibre with 20 µm in diameter core suitable for amplifying the beam generated in oscillator. We implemented made in-house endcaps to prove the utility of the fibre towards high peak power applications. Full Text: PDF ReferencesStrategies Unlimited, The Worldwide Market for Lasers: Market Review and Forecast, 2020 DirectLink J. Zhu, P. Zhou, Y. Ma, X. Xu, and Z. Liu, "Power scaling analysis of tandem-pumped Yb-doped fiber lasers and amplifiers", Opt. Express 19, 18645 (2011) CrossRef IPG Photonics, Product information, accessed: October, 2020. DirectLink J.W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, "Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power", Opt. Express 16, 13240 (2008) CrossRef W. Koechner, "Solid-State Laser Engineering", Springer Series in Optical Science, Berlin 1999 CrossRef A. V. Smith, and B. T. Do, "Bulk and surface laser damage of silica by picosecond and nanosecond pulses at 1064 nm", Appl. Opt. 47, 4812 (2008), CrossRef M. N. Zervas, C. Codemard, "High Power Fiber Lasers: A Review", IEEE J. Sel. Top. Quantum Electron. 20, 1, 2014 CrossRef D.J. Richardson, J. Nilsson, and W.A. Clarkson, "High power fiber lasers: current status and future perspectives [Invited]", J. Opt. Soc. Am. B, 27, 63, 2010, CrossRef M. Li, X. Chen, A. Liu, S. Gray, J. Wang, D. T. Walton; L. A. Zenteno, "Limit of Effective Area for Single-Mode Operation in Step-Index Large Mode Area Laser Fibers", J. Lightw. Technol., 27, 3010, 2009, CrossRef J. Limpert, S. Hofer, A. Liem, H. Zellmer, A. Tunnermann., S. Knoke, and H. Voelckel, "100-W average-power, high-energy nanosecond fiber amplifier", App.Phys.B 75, 477, 2002, CrossRef

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Im, Mee Seong, Chun-Ju Lai, and Arik Wilbert. "A study of irreducible components of Springer fibers using quiver varieties." Journal of Algebra 591 (February 2022): 217–48. http://dx.doi.org/10.1016/j.jalgebra.2021.10.019.

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Mellit. "Poincaré polynomials of character varieties, Macdonald polynomials and affine Springer fibers." Annals of Mathematics 192, no. 1 (2020): 165. http://dx.doi.org/10.4007/annals.2020.192.1.3.

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Arinkin, D., and D. Gaitsgory. "The category of singularities as a crystal and global Springer fibers." Journal of the American Mathematical Society 31, no. 1 (May 8, 2017): 135–214. http://dx.doi.org/10.1090/jams/882.

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Hikita, Tatsuyuki. "Affine Springer fibers of type A and combinatorics of diagonal coinvariants." Advances in Mathematics 263 (October 2014): 88–122. http://dx.doi.org/10.1016/j.aim.2014.06.011.

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Kim, Dongkwan. "Springer Fibers for the Minimal and the Minimal Special Nilpotent Orbits." Algebras and Representation Theory 22, no. 3 (April 30, 2018): 545–67. http://dx.doi.org/10.1007/s10468-018-9786-4.

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Kumar, Shrawan, and Claudio Procesi. "An algebro-geometric realization of equivariant cohomology of some Springer fibers." Journal of Algebra 368 (October 2012): 70–74. http://dx.doi.org/10.1016/j.jalgebra.2012.06.019.

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Fresse, Lucas, Ronit Mansour, and Anna Melnikov. "Unimodality of the distribution of Betti numbers for some Springer fibers." Journal of Algebra 391 (October 2013): 284–304. http://dx.doi.org/10.1016/j.jalgebra.2013.05.018.

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Varagnolo, M., and E. Vasserot. "Finite-dimensional representations of DAHA and affine Springer fibers: The spherical case." Duke Mathematical Journal 147, no. 3 (April 2009): 439–540. http://dx.doi.org/10.1215/00127094-2009-016.

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