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Journal articles on the topic 'Cyclotomic Hecke algebras'

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Published: 4 June 2021
Last updated: 20 February 2023

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1

Rostam, Salim. "Cyclotomic Yokonuma–Hecke algebras are cyclotomic quiver Hecke algebras." Advances in Mathematics 311 (April 2017): 662–729. http://dx.doi.org/10.1016/j.aim.2017.03.004.

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2

OGIEVETSKY, O. V., and L. POULAIN D'ANDECY. "ON REPRESENTATIONS OF CYCLOTOMIC HECKE ALGEBRAS." Modern Physics Letters A 26, no. 11 (April 10, 2011): 795–803. http://dx.doi.org/10.1142/s0217732311035377.

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An approach, based on Jucys–Murphy elements, to the representation theory of cyclotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke algebra) of the set of the Jucys–Murphy elements is established. A basis of the cyclotomic Hecke algebra is suggested; this basis is used to establish the flatness of the deformation without using the representation theory.
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3

Poulain d'Andecy, L., and R. Walker. "Affine Hecke algebras and generalizations of quiver Hecke algebras of type B." Proceedings of the Edinburgh Mathematical Society 63, no. 2 (March 9, 2020): 531–78. http://dx.doi.org/10.1017/s0013091519000294.

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AbstractWe define and study cyclotomic quotients of affine Hecke algebras of type B. We establish an isomorphism between direct sums of blocks of these algebras and a generalization, for type B, of cyclotomic quiver Hecke algebras, which are a family of graded algebras closely related to algebras introduced by Varagnolo and Vasserot. Inspired by the work of Brundan and Kleshchev, we first give a family of isomorphisms for the corresponding result in type A which includes their original isomorphism. We then select a particular isomorphism from this family and use it to prove our result.
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4

König, Steffen. "Cyclotomic Schur Algebras and Blocks of Cyclic Defect." Canadian Mathematical Bulletin 43, no. 1 (March 1, 2000): 79–86. http://dx.doi.org/10.4153/cmb-2000-012-0.

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5

Rouquier, Raphaël. "Quiver Hecke Algebras and 2-Lie Algebras." Algebra Colloquium 19, no. 02 (May 3, 2012): 359–410. http://dx.doi.org/10.1142/s1005386712000247.

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We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with the resulting monoidal categories, which have a geometric description via quiver varieties, in certain cases. We present basic properties of 2-representations and describe simple 2-representations, via cyclotomic quiver Hecke algebras, and through microlocalized quiver varieties.
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6

Malle, Gunter, and Andrew Mathas. "Symmetric Cyclotomic Hecke Algebras." Journal of Algebra 205, no. 1 (July 1998): 275–93. http://dx.doi.org/10.1006/jabr.1997.7339.

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7

Chlouveraki, Maria. "Rouquier blocks of the cyclotomic Hecke algebras of G(de, e, r)." Nagoya Mathematical Journal 197 (March 2010): 175–212. http://dx.doi.org/10.1215/00277630-2009-004.

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The Rouquier blocks of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the families of characters defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite series G(de, e, r), thus completing their calculation for all complex reflection groups.
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8

Chlouveraki, Maria. "Rouquier blocks of the cyclotomic Hecke algebras of G(de, e, r)." Nagoya Mathematical Journal 197 (March 2010): 175–212. http://dx.doi.org/10.1017/s0027763000009880.

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The Rouquier blocks of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the families of characters defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite seriesG(de, e, r), thus completing their calculation for all complex reflection groups.
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9

Savage, Alistair. "Affine Wreath Product Algebras." International Mathematics Research Notices 2020, no. 10 (May 24, 2018): 2977–3041. http://dx.doi.org/10.1093/imrn/rny092.

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Abstract We study the structure and representation theory of affine wreath product algebras and their cyclotomic quotients. These algebras, which appear naturally in Heisenberg categorification, simultaneously unify and generalize many important algebras appearing in the literature. In particular, special cases include degenerate affine Hecke algebras, affine Sergeev algebras (degenerate affine Hecke–Clifford algebras), and wreath Hecke algebras. In some cases, specializing the results of the current paper recovers known results, but with unified and simplified proofs. In other cases, we obtain new results, including proofs of two open conjectures of Kleshchev and Muth.
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10

Alexander BRAVERMAN, Pavel ETINGOF, and Michael FINKELBERG. "Cyclotomic double affine Hecke algebras." Annales scientifiques de l'École normale supérieure 53, no. 5 (2020): 1249–312. http://dx.doi.org/10.24033/asens.2446.

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11

Lyle, Sinéad, and Andrew Mathas. "Blocks of cyclotomic Hecke algebras." Advances in Mathematics 216, no. 2 (December 2007): 854–78. http://dx.doi.org/10.1016/j.aim.2007.06.008.

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12

Rostam, Salim. "Cyclotomic quiver Hecke algebras and Hecke algebra of $G(r,p,n)$." Transactions of the American Mathematical Society 371, no. 6 (November 16, 2018): 3877–916. http://dx.doi.org/10.1090/tran/7485.

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13

Brundan, Jonathan, and Alexander Kleshchev. "Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras." Inventiones mathematicae 178, no. 3 (June 4, 2009): 451–84. http://dx.doi.org/10.1007/s00222-009-0204-8.

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14

Mathas, Andrew. "Restricting Specht modules of cyclotomic Hecke algebras." Science China Mathematics 61, no. 2 (September 15, 2017): 299–310. http://dx.doi.org/10.1007/s11425-016-9032-2.

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15

Zhao, Deke. "Schur elements of degenerate cyclotomic Hecke algebras." Israel Journal of Mathematics 205, no. 1 (December 16, 2014): 485–507. http://dx.doi.org/10.1007/s11856-014-1140-x.

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16

Brundan, Jonathan, and Alexander Kleshchev. "Graded decomposition numbers for cyclotomic Hecke algebras." Advances in Mathematics 222, no. 6 (December 2009): 1883–942. http://dx.doi.org/10.1016/j.aim.2009.06.018.

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17

Chlouveraki, Maria. "Rouquier blocks of the cyclotomic Hecke algebras." Comptes Rendus Mathematique 344, no. 10 (May 2007): 615–20. http://dx.doi.org/10.1016/j.crma.2007.04.002.

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18

Zhao, Deke, and Yanbo Li. "Fusion Procedure for Degenerate Cyclotomic Hecke Algebras." Algebras and Representation Theory 18, no. 2 (September 19, 2014): 449–61. http://dx.doi.org/10.1007/s10468-014-9503-x.

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19

Boys, Clinton. "Semisimple Representations of Alternating Cyclotomic Hecke Algebras." Algebras and Representation Theory 19, no. 1 (September 11, 2015): 235–53. http://dx.doi.org/10.1007/s10468-015-9572-5.

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20

CHLOUVERAKI, MARIA, and NICOLAS JACON. "SCHUR ELEMENTS AND BASIC SETS FOR CYCLOTOMIC HECKE ALGEBRAS." Journal of Algebra and Its Applications 10, no. 05 (October 2011): 979–93. http://dx.doi.org/10.1142/s0219498811005075.

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We study the Schur elements and the a-function for cyclotomic Hecke algebras. As a consequence, we show the existence of canonical basic sets, as defined by Geck–Rouquier, for certain complex reflection groups. This includes the case of finite Weyl groups for all choices of parameters (in characteristic 0).
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21

He, Zhekun, Jun Hu, and Huang Lin. "Trace forms on the cyclotomic Hecke algebras and cocenters of the cyclotomic Schur algebras." Journal of Pure and Applied Algebra 227, no. 4 (April 2023): 107281. http://dx.doi.org/10.1016/j.jpaa.2022.107281.

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22

Kleshchev, Alexander S., Andrew Mathas, and Arun Ram. "Universal graded Specht modules for cyclotomic Hecke algebras." Proceedings of the London Mathematical Society 105, no. 6 (June 19, 2012): 1245–89. http://dx.doi.org/10.1112/plms/pds019.

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23

Rouquier, Raphaël, Peng Shan, Michela Varagnolo, and Eric Vasserot. "Categorifications and cyclotomic rational double affine Hecke algebras." Inventiones mathematicae 204, no. 3 (September 15, 2015): 671–786. http://dx.doi.org/10.1007/s00222-015-0623-7.

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24

Rui, Hebing. "Weights of Markov Traces on Cyclotomic Hecke Algebras." Journal of Algebra 238, no. 2 (April 2001): 762–75. http://dx.doi.org/10.1006/jabr.2000.8636.

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25

Lee, Dong-il. "Cyclotomic Hecke Algebras of G(r, p, n)." Algebras and Representation Theory 13, no. 6 (December 15, 2009): 705–18. http://dx.doi.org/10.1007/s10468-009-9170-5.

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26

Chlouveraki, Maria, and Hyohe Miyachi. "Decomposition matrices for d-Harish-Chandra series: the exceptional rank two cases." LMS Journal of Computation and Mathematics 14 (November 1, 2011): 271–90. http://dx.doi.org/10.1112/s1461157010000306.

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AbstractWe calculate all decomposition matrices of the cyclotomic Hecke algebras of the rank two exceptional complex reflection groups in characteristic zero. We prove the existence of canonical basic sets in the sense of Geck–Rouquier and show that all modular irreducible representations can be lifted to the ordinary ones.
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27

Vazirani, M. "Filtrations on the Mackey decomposition for cyclotomic Hecke algebras." Journal of Algebra 252, no. 2 (June 2002): 205–27. http://dx.doi.org/10.1016/s0021-8693(02)00075-3.

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28

Rui, Hebing, and Linliang Song. "Isomorphisms between simple modules of degenerate cyclotomic Hecke algebras." Journal of Algebra 483 (August 2017): 329–61. http://dx.doi.org/10.1016/j.jalgebra.2017.03.034.

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29

Mackaay, Marco, and Alistair Savage. "Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification." Journal of Algebra 505 (July 2018): 150–93. http://dx.doi.org/10.1016/j.jalgebra.2018.03.004.

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30

Zhou, Kai, and Jun Hu. "On some embeddings between the cyclotomic quiver Hecke algebras." Proceedings of the American Mathematical Society 148, no. 2 (August 7, 2019): 495–511. http://dx.doi.org/10.1090/proc/14733.

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31

Chlouveraki, Maria, and Loïc Poulain d'Andecy. "Markov Traces on Affine and Cyclotomic Yokonuma–Hecke Algebras." International Mathematics Research Notices 2016, no. 14 (October 1, 2015): 4167–228. http://dx.doi.org/10.1093/imrn/rnv257.

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32

Varagnolo, M., and E. Vasserot. "Cyclotomic double affine Hecke algebras and affine parabolic category O." Advances in Mathematics 225, no. 3 (October 2010): 1523–88. http://dx.doi.org/10.1016/j.aim.2010.03.028.

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33

Ariki, Susumu. "Proof of the modular branching rule for cyclotomic Hecke algebras." Journal of Algebra 306, no. 1 (December 2006): 290–300. http://dx.doi.org/10.1016/j.jalgebra.2006.04.033.

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34

Hu, Jun, and Andrew Mathas. "Seminormal forms and cyclotomic quiver Hecke algebras of type A." Mathematische Annalen 364, no. 3-4 (July 4, 2015): 1189–254. http://dx.doi.org/10.1007/s00208-015-1242-8.

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35

Cantrell, Andy, Tom Halverson, and Brian Miller. "Robinson–Schensted–Knuth insertion and characters of cyclotomic Hecke algebras." Journal of Combinatorial Theory, Series A 99, no. 1 (July 2002): 17–31. http://dx.doi.org/10.1006/jcta.2002.3252.

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36

Shan, P., M. Varagnolo, and E. Vasserot. "Koszul duality of affine Kac–Moody algebras and cyclotomic rational double affine Hecke algebras." Advances in Mathematics 262 (September 2014): 370–435. http://dx.doi.org/10.1016/j.aim.2014.05.012.

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37

Kerschl, Alexander Ferdinand. "On simple modules of cyclotomic quiver Hecke algebras of type A." Advances in Mathematics 390 (October 2021): 107852. http://dx.doi.org/10.1016/j.aim.2021.107852.

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38

Rostam, Salim, and Loïc Poulain d'Andecy. "Morita equivalences for cyclotomic Hecke algebras of type B and D." Bulletin de la Société Mathématique de France 149, no. 1 (2021): 179–233. http://dx.doi.org/10.24033/bsmf.2828.

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39

Shan, Peng. "Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras." Annales scientifiques de l'École normale supérieure 44, no. 1 (2011): 147–82. http://dx.doi.org/10.24033/asens.2141.

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40

Brundan, Jonathan. "Centers of degenerate cyclotomic Hecke algebras and parabolic category $\mathcal O$." Representation Theory of the American Mathematical Society 12, no. 10 (July 29, 2008): 236–59. http://dx.doi.org/10.1090/s1088-4165-08-00333-6.

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41

Chlouveraki, Maria. "Degree and valuation of the Schur elements of cyclotomic Hecke algebras." Journal of Algebra 320, no. 11 (December 2008): 3935–49. http://dx.doi.org/10.1016/j.jalgebra.2008.07.024.

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42

Evseev, Anton. "On graded decomposition numbers for cyclotomic Hecke algebras in quantum characteristic 2." Bulletin of the London Mathematical Society 46, no. 4 (April 30, 2014): 725–31. http://dx.doi.org/10.1112/blms/bdu028.

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43

Lambropoulou, Sofia. "Knot theory related to generalized and cyclotomic Hecke algebras of type ℬ." Journal of Knot Theory and Its Ramifications 08, no. 05 (August 1999): 621–58. http://dx.doi.org/10.1142/s0218216599000419.

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44

Ogievetsky, O. V., and L. Poulain d’Andecy. "Induced representations and traces for chains of affine and cyclotomic Hecke algebras." Journal of Geometry and Physics 87 (January 2015): 354–72. http://dx.doi.org/10.1016/j.geomphys.2014.07.005.

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45

Kim, SungSoon. "Families of the characters of the cyclotomic Hecke algebras of G(de,e,r)." Journal of Algebra 289, no. 2 (July 2005): 346–64. http://dx.doi.org/10.1016/j.jalgebra.2005.03.022.

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46

Hu, Jun, and Shixuan Wang. "On the seminormal bases and dual seminormal bases of the cyclotomic Hecke algebras of type G(ℓ,1,n)." Journal of Algebra 600 (June 2022): 195–221. http://dx.doi.org/10.1016/j.jalgebra.2022.01.039.

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47

McGerty, Kevin. "On the centre of the cyclotomic Hecke algebra of G(m, 1, 2)." Proceedings of the Edinburgh Mathematical Society 55, no. 2 (April 12, 2012): 497–506. http://dx.doi.org/10.1017/s0013091510001264.

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AbstractWe compute the centre of the cyclotomic Hecke algebra attached to G(m, 1, 2) and show that if q ≠ 1, it is equal to the image of the centre of the affine Hecke algebra Haff2. We also briefly discuss what is known about the relation between the centre of an arbitrary cyclotomic Hecke algebra and the centre of the affine Hecke algebra of type A.
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48

Speyer, Liron. "On the semisimplicity of the cyclotomic quiver Hecke algebra of type $C$." Proceedings of the American Mathematical Society 146, no. 5 (December 4, 2017): 1845–57. http://dx.doi.org/10.1090/proc/13876.

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49

Mathas, Andrew. "Positive Jantzen sum formulas for cyclotomic Hecke algebras." Mathematische Zeitschrift, March 2, 2022. http://dx.doi.org/10.1007/s00209-021-02957-7.

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AbstractThis paper proves a “positive” Jantzen sum formula for the Specht modules of the cyclotomic Hecke algebras of type A and uses it to obtain new bounds on decomposition numbers. Quite remarkably, our results are proved entirely inside the cyclotomic Hecke algebras. Our positive sum formula shows that, in the Grothendieck group, the Jantzen sum formula can be written as an explicit non-negative linear combination of modules $$[E^{\varvec{\nu }}_{f,e}]$$ [ E f , e ν ] , which are the modular reductions of simple modules of related Hecke algebras in characteristic zero. The coefficient of $$[E^{\varvec{\nu }}_{f,e}]$$ [ E f , e ν ] in the sum formula is determined by the graded decomposition numbers in characteristic zero, which are known, and by the characteristic of the field. As a consequence we give an explicit upper bound for the decomposition numbers in characteristic $$p>0$$ p > 0 in terms of linear combinations of decomposition numbers of a cyclotomic Hecke algebra at $$ep^r$$ e p r th roots of unity in characteristic zero, for $$r\ge 0$$ r ≥ 0 . Finally, we prove a new and more elegant “classical” Jantzen sum formula for these algebras.
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50

Gurevich, Maxim. "Graded Specht Modules as Bernstein–Zelevinsky Derivatives of the RSK Model." International Mathematics Research Notices, August 13, 2022. http://dx.doi.org/10.1093/imrn/rnac222.

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Abstract We clarify the links between the graded Specht construction of modules over cyclotomic Hecke algebras and the Robinson-Schensted-Knuth (RSK) construction for quiver Hecke algebras of type $A$, which was recently imported from the setting of representations of $p$-adic groups. For that goal we develop a theory of crystal derivative operators on quiver Hecke algebra modules that categorifies the Berenstein–Zelevinsky strings framework on quantum groups and generalizes a graded variant of the classical Bernstein–Zelevinsky derivatives from the $p$-adic setting. Graded cyclotomic decomposition numbers are shown to be a special subfamily of the wider concept of RSK decomposition numbers.
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