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Academic literature on the topic 'Coadjoint orbits'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Coadjoint orbits"

1

Kurniadi, Edi. "Ruang Fase Tereduksi Grup Lie Aff (1)." Jambura Journal of Mathematics 3, no. 2 (June 24, 2021): 180–86. http://dx.doi.org/10.34312/jjom.v3i2.10653.

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ABSTRAKDalam artikel ini dipelajari ruang fase tereduksi dari suatu grup Lie khususnya untuk grup Lie affine berdimensi 2. Tujuannya adalah untuk mengidentifikasi ruang fase tereduksi dari melalui orbit coadjoint buka di titik tertentu pada ruang dual dari aljabar Lie . Aksi dari grup Lie pada ruang dual menggunakan representasi coadjoint. Hasil yang diperoleh adalah ruang Fase tereduksi tiada lain adalah orbit coadjoint-nya yang buka di ruang dual . Selanjutnya, ditunjukkan pula bahwa grup Lie affine tepat mempunyai dua buah orbit coadjoint buka. Hasil yang diperoleh dalam penelitian ini dapat diperluas untuk kasus grup Lie affine berdimensi dan untuk kasus grup Lie lainnya.ABSTRACTIn this paper, we study a reduced phase space for a Lie group, particularly for the 2-dimensional affine Lie group which is denoted by Aff (1). The work aims to identify the reduced phase space for Aff (1) by open coadjoint orbits at certain points in the dual space aff(1)* of the Lie algebra aff(1). The group action of Aff(1) on the dual space aff(1)* is considered using coadjoint representation. We obtained that the reduced phase space for the affine Lie group Aff(1) is nothing but its open coadjoint orbits. Furthermore, we show that the affine Lie group Aff (1) exactly has two open coadjoint orbits in aff(1)*. Our result can be generalized for the n(n+1) dimensional affine Lie group Aff(n) and for another Lie group.

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GORSKY, A., and A. JOHANSEN. "LIOUVILLE THEORY AND SPECIAL COADJOINT VIRASORO ORBITS." International Journal of Modern Physics A 10, no. 06 (March 10, 1995): 785–99. http://dx.doi.org/10.1142/s0217751x95000371.

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We describe the Hamiltonian reduction of the coadjoint Kac–Moody orbits to the Virasoro coadjoint orbits explicitly in terms of the Lagrangian approach for the Wess–Zumino–Novikov–Witten theory. While a relation of the coadjoint Virasoro orbit Diff S1/ SL (2, R) to the Liouville theory has already been studied, we analyze the role of special coadjoint Virasoro orbits Diff [Formula: see text]corresponding to stabilizers generated by the vector fields with double zeros. The orbits with stabilizers with single zeros do not appear in the model. We find an interpretation of zeros xi of the vector field of stabilizer [Formula: see text] and additional parameters qi, i = 1, …, n, in terms of quantum mechanics for n-point particles on the circle. We argue that the special orbits are generated by insertions of "wrong sign" Liouville exponential into the path integral. The additional parmeters qi are naturally interpreted as accessory parameters for the uniformization map. Summing up the contributions of the special Virasoro orbits we get the integrable sinh–Gordon type theory.

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LIEDÓ, M. A. "DEFORMATION QUANTIZATION OF COADJOINT ORBITS." International Journal of Modern Physics B 14, no. 22n23 (September 20, 2000): 2397–400. http://dx.doi.org/10.1142/s0217979200001916.

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A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.

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BOŽIČEVIĆ, MLADEN. "A LIMIT FORMULA FOR EVEN NILPOTENT ORBITS." International Journal of Mathematics 19, no. 02 (February 2008): 223–36. http://dx.doi.org/10.1142/s0129167x08004650.

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Let Gℝ be a real form of a complex, semisimple Lie group G. Assume [Formula: see text] is an even nilpotent coadjoint Gℝ-orbit. We prove a limit formula, expressing the canonical measure on [Formula: see text] as a limit of canonical measures on semisimple coadjoint orbits, where the parameter of orbits varies over the negative chamber defined by the parabolic subalgebra associated with [Formula: see text].

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5

Arnal, D., M. Cahen, and S. Gutt. "Deformations on coadjoint orbits." Journal of Geometry and Physics 3, no. 3 (January 1986): 327–51. http://dx.doi.org/10.1016/0393-0440(86)90013-6.

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6

Robinson, P. L. "Equivariant prequantization and admissible coadjoint orbits." Mathematical Proceedings of the Cambridge Philosophical Society 114, no. 1 (July 1993): 131–42. http://dx.doi.org/10.1017/s0305004100071462.

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The orbit method has as its primary goal the construction and parametrization of the irreducible unitary representations of a (simply-connected) Lie group in terms of its coadjoint orbits. This goal was achieved with complete success for nilpotent groups by Kirillov[8] and for type I solvable groups by Auslander and Kostant[l] but is known to encounter difficulties when faced with more general groups. Geometric quantization can be viewed as an outgrowth of the orbit method aimed at providing a geometric passage from classical mechanics to quantum mechanics. Whereas the original geometric quantization scheme due to Kostant[9] and Souriau[14] enabled such a passage in a variety of situations, it too encounters difficulties in broader contexts.

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Božičević, Mladen. "Invariant measures on nilpotent orbits associated with holomorphic discrete series." Representation Theory of the American Mathematical Society 25, no. 24 (August 18, 2021): 732–47. http://dx.doi.org/10.1090/ert/580.

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Let G R G_\mathbb R be a real form of a complex, semisimple Lie group G G . Assume G R G_\mathbb R has holomorphic discrete series. Let W \mathcal W be a nilpotent coadjoint G R G_\mathbb R -orbit contained in the wave front set of a holomorphic discrete series. We prove a limit formula, expressing the canonical measure on W \mathcal W as a limit of canonical measures on semisimple coadjoint orbits, where the parameter of orbits varies over the positive chamber defined by the Borel subalgebra associated with holomorphic discrete series.

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8

Esposito, Chiara, Philipp Schmitt, and Stefan Waldmann. "Comparison and continuity of Wick-type star products on certain coadjoint orbits." Forum Mathematicum 31, no. 5 (September 1, 2019): 1203–23. http://dx.doi.org/10.1515/forum-2018-0302.

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AbstractIn this paper, we discuss continuity properties of the Wick-type star product on the 2-sphere, interpreted as a coadjoint orbit. Star products on coadjoint orbits in general have been constructed by different techniques. We compare the constructions of Alekseev–Lachowska and Karabegov, and we prove that they agree in general. In the case of the 2-sphere, we establish the continuity of the star product, thereby allowing for a completion to a Fréchet algebra.

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9

Vi�a, A. "Cohomological splitting of coadjoint orbits." Archiv der Mathematik 82, no. 1 (January 1, 2004): 13–15. http://dx.doi.org/10.1007/s00013-003-4819-5.

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10

Le Bruyn, Lieven. "Noncommutative smoothness and coadjoint orbits." Journal of Algebra 258, no. 1 (December 2002): 60–70. http://dx.doi.org/10.1016/s0021-8693(02)00533-1.

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Dissertations / Theses on the topic "Coadjoint orbits"

1

Mihov, Diko. "Quantization of nilpotent coadjoint orbits." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38410.

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Li, Zongyi. "Coadjoint orbits and induced representations." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/43270.

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Astashkevich, Alexander. "Fedosov's quantization of semisimple coadjoint orbits." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/38396.

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4

Dai, Jialing. "Conjugacy classes, characters and coadjoint orbits of Diff⁺S¹." Diss., The University of Arizona, 2000. http://hdl.handle.net/10150/284342.

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The principal motivation of this dissertation is to understand the unitary irreducible representations and characters of Dif f⁺S¹-the group of all orientation-preserving diffeomorphisms of S¹ by studying conjugacy classes of Dif f⁺S¹ and its coadjoint orbits. For this purpose, we mainly focus on the following two topics. The first is to study the relation between a real Lie group G and its associated complex semigroup S(G), which was initiated by Oshansky. We consider two particular examples: (1) PSU(1.1) and PSL(2, C)⁺ (Chapter 1); (2) D and A (Chapter 2). We have shown that (a) The equivalence classes determined by the function q on PSL(2, C)⁺ (resp. A) are the same as the conjugacy classes in PSL(2, C)⁺ (resp. A ). In fact the restriction of q to PSL(2, C)⁺ equals the square of the "smaller" of the two eigenvalues of an element in PSL(2, C)+. (b) The fact that the representation of PSL(2, C)⁺ is of trace class makes the character of PSL(2, C)⁺ well-defined. Moreover the character of PSL(2, C)⁺ has analytic continuation onto PSU(1,1) except on a set of measure zero. Surprisingly, the extended characters are exactly Harish-Chandra global characters Xᵐ(PSU)₍₁.₁₎ =Θm. Secondly, we investigate the coadjoint orbits of Virasoro group-the central extension of Dif f⁺S¹ (Chapter 3), which has been considered before by Segal, Kirillov and (later) Witten. We improved Segal's result by parameterizing coadjoint orbits precisely in terms of following conjugacy classes in P͂S͂U͂(1,1): Par⁺₀,{n,n ∈ N},{Elln, n∈N},{Par⁽⁺/⁻⁾(n),n > 0}, {Hyp(n),n ≥ }0. We also completed Kirillov's list of representatives of coadjoint orbits, and we fleshed out the connection between Segal's and Kirillov's and Witten's work by giving the correspondence between conjugacy classes in P͂S͂U͂ (1,1) and the representatives of coadjoint orbits and stabilizers.

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André, Carlos Alberto Martins. "Irreducible characters of the unitriangular group and coadjoint orbits." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/110600/.

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The method of coadjoint orbits was introduced by Kirillov to study the unitary irreducible representations of a nilpotent Lie groups. Afterwards Kazhdan adapted this method to determine the irreducible complex characters of a finite unipotent group. We use this method to study the irreducible complex characters of any finite unitriangular group. In chapters 2 and 5 we established an orthogonal decomposition of the regular character of any finite unitriangular group. Chapters 3 and 4 are concerned with coadjoint orbits of any unitriangular group defined over an algebraically closed field. Chapter 3 is essentially the orbit version of chapter 2. In fact we obtain a decomposition of the dual space of the niltriangular Lie algebra as a disjoint union of invariant subvarieties. In a certain sense this decomposition corresponds to the one obtained in chapter 2 and 5.

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Nevins, Monica 1973. "Admissible nilpotent coadjoint orbits of p-adic reductive Lie groups." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47467.

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Plummer, Michael. "Stratified fibre bundles and symplectic reduction on coadjoint orbits of SU(n)." Thesis, University of Surrey, 2008. http://epubs.surrey.ac.uk/842671/.

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The problem of classifying the reduced phase spaces of the natural torus action on a generic coadjoint orbit of SU(n) is considered. The concept of a stratified fibre bundle is defined. It is proved that the orbit map of an equivariant fibre bundle is a stratified fibre bundle. This result is then used to give an iterative description of the reduced phase spaces of the torus action on a generic coadjoint orbit of SU(n). The theory is illustrated with a detailed examination of the n = 3 case, that of the two torus action on a coadjoint orbit of SU(3).

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Villa, Patrick Björn [Verfasser], Peter [Akademischer Betreuer] Heinzner, and Alan T. [Akademischer Betreuer] Huckleberry. "Kählerian structures of coadjoint orbits of semisimple Lie groups and their orbihedra / Patrick Björn Villa. Gutachter: Peter Heinzner ; Alan T. Huckleberry." Bochum : Ruhr-Universität Bochum, 2015. http://d-nb.info/1079843477/34.

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9

Deltour, Guillaume. "Propriétés symplectiques et hamiltoniennes des orbites coadjointes holomorphes." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2010. http://tel.archives-ouvertes.fr/tel-00552150.

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L'objet de cette thèse est l'étude de la structure symplectique des orbites coadjointes holomorphes, et de leurs projections. Une orbite coadjointe holomorphe O est une orbite coadjointe elliptique d'un groupe de Lie réel semi-simple, connexe, non compact et à centre fini, provenant d'un espace symétrique hermitien G/K, telle que O puisse être naturellement munie d'une structure kählérienne G-invariante. Ces orbites sont une généralisation de l'espace symétrique hermitien G/K. Dans cette thèse, nous prouvons que le symplectomorphisme de McDuff se généralise aux orbites coadjointes holomorphes, décrivant la structure symplectique de l'orbite O par le produit direct d'une orbite coadjointe compacte et d'un espace vectoriel symplectique. Ce symplectomorphisme est ensuite utilisé pour déterminer les équations de la projection de l'orbite O relative au sous-groupe compact maximal K de G, en faisant intervenir des résultats récents de Ressayre en Théorie Géométrique des Invariants.

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Zergane, Amel. "Séparation des représentations des groupes de Lie par des ensembles moments." Thesis, Dijon, 2011. http://www.theses.fr/2011DIJOS086/document.

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Si (π, H) est une représentation unitaire irréductible d'un groupe de Lie G, on sait lui associer son application moment Ψπ. La fermeture de l'image de Ψπ s'appelle l'ensemble moment de π. Généralement, cet ensemble est Conv(Oπ), si Oπ est l'orbite coadjointe associée à π. Mais il ne caractérise pas π : deux orbites distinctes peuvent avoir la même enveloppe convexe fermée. On peut contourner cette non séparation en considérant un surgroupe G+ de G et une application non linéaire ø de g* dans (g+)* telle que, pour les orbites générique, ø(O) est une orbite et Conv (ø(O)) caractérise O. Dans cette thèse, on montre que l'on peut choisir le couple (G+, ø), avec ø de degré ≤ 2 pour tous les groupes nilpotents de dimension ≤ 6, à une exception près, tous les groupes résolubles de dimension ≤ 4, et pour un exemple de groupe de déplacements. Ensuite, on étudie le cas des groupes G = SL(n, R). Pour ces groupes, il existe un tel couple avec ø de degré n, mais il n'en existe pas avec ø de degré 2 si n>2, il n'en existe pas avec ø de degré 3 si n=4. Enfin, on montre que l'application moment Ψπ est celle d'une action fortement hamiltonienne de G sur la variété de Fréchet symplectique PH∞. On construit un foncteur qui associe à tout G un surgroupe de Lie Fréchet G̃, de dimension infinie et, à tout π de G, une action π̃ fortement hamiltonienne, dont l'ensemble moment caractérise π
To a unitary irreducible representation (π,H) of a Lie group G, is associated a moment map Ψπ. The closure of the range of Ψπ is the moment set of π. Generally, this set is Conv(Oπ), if Oπ is the corresponding coadjoint orbit. Unfortunately, it does not characterize π : 2 distincts orbits can have the same closed convex hull. We can overpass this di culty, by considering an overgroup G+ for G and a non linear map ø from g* into (g+)* such that, for generic orbits, ø(O) is an orbit and Conv( ø(O)) characterizes O. In the present thesis, we show that we can choose the pair (G+,ø), with deg ø ≤2 for all the nilpotent groups with dimension ≤6, except one, for all solvable groups with diemnsion ≤4, and for an example of motion group. Then we study the G=SL(n,R) case. For these groups, there exists ø with deg ø =n, if n>2, there is no such ø with deg ø=2, if n=4, there is no such ø with deg ø=3. Finally, we show that the moment map Ψπ is coming from a stronly Hamiltonian G-action on the Frécht symplectic manifold PH∞. We build a functor, which associates to each G an infi nite diemnsional Fréchet-Lie overgroup G̃,and, to each π a strongly Hamiltonian action, whose moment set characterizes π

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Books on the topic "Coadjoint orbits"

1

André, Carlos Alberto Martins. Irreducible characters of the unitriangular group and coadjoint orbits. [s.l.]: typescript, 1992.

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2

1943-, Seitz Gary M., ed. Unipotent and nilpotent classes in simple algebraic groups and lie algebras. Providence, R.I: American Mathematical Society, 2012.

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Book chapters on the topic "Coadjoint orbits"

1

Marsden, Jerrold E., and Tudor S. Ratiu. "Coadjoint Orbits." In Texts in Applied Mathematics, 443–79. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-0-387-21792-5_14.

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Marsden, Jerrold E., and Tudor S. Ratiu. "Coadjoint Orbits." In Texts in Applied Mathematics, 399–430. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-2682-6_14.

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3

Oblak, Blagoje. "Virasoro Coadjoint Orbits." In Springer Theses, 201–40. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61878-4_7.

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4

Kirillov, A. "Geometry of coadjoint orbits." In Graduate Studies in Mathematics, 1–29. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/gsm/064/01.

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Oblak, Blagoje. "Coadjoint Orbits and Geometric Quantization." In Springer Theses, 109–60. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61878-4_5.

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Dwivedi, Shubham, Jonathan Herman, Lisa C. Jeffrey, and Theo van den Hurk. "The Symplectic Structure on Coadjoint Orbits." In SpringerBriefs in Mathematics, 27–29. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-27227-2_5.

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Graham, William, and David A. Vogan. "Geometric Quantization for Nilpotent Coadjoint Orbits." In Progress in Mathematics, 69–137. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-4162-1_6.

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Adams, M. R., J. Harnad, and J. Hurtubise. "Coadjoint Orbits, Spectral Curves and Darboux Coordinates." In Mathematical Sciences Research Institute Publications, 9–21. New York, NY: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4613-9725-0_2.

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Lozano, Yolanda, Steven Duplij, Malte Henkel, Malte Henkel, Euro Spallucci, Steven Duplij, Malte Henkel, et al. "Supersymmetry Methods, particle dynamics on coadjoint orbits." In Concise Encyclopedia of Supersymmetry, 472–73. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_631.

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Astashkevich, Alexander. "On Karabegov’s Quantizations of Semisimple Coadjoint Orbits." In Advances in Geometry, 1–18. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1770-1_1.

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Conference papers on the topic "Coadjoint orbits"

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GOLDIN, GERALD A. "QUANTIZATION ON COADJOINT ORBITS OF DIFFEOMORPHISM GROUPS: SOME RESEARCH DIRECTIONS." In Proceedings of XI Workshop on Geometric Methods in Physics. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814440844_0007.

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Iglesias-Zemmour, Patrick. "Every Symplectic Manifold Is A Coadjoint Orbit." In Frontiers of Fundamental Physics 14. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.224.0141.

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Oh, Phillial. "Field Theory on Coadjoint Orbit and Self-Dual Chern-Simons Solitons." In Proceedings of the APCTP Winter School. WORLD SCIENTIFIC, 1998. http://dx.doi.org/10.1142/9789814447287_0010.

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Reports on the topic "Coadjoint orbits"

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Bernatska, Julia. Geometry and Topology of Coadjoint Orbits of Semisimple Lie Groups. GIQ, 2012. http://dx.doi.org/10.7546/giq-9-2008-146-166.

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