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Representations of quiver Hecke algebras via Lyndon bases.(English)Zbl 1264.20006

This paper completes the classification of simple modules over quiver Hecke algebras (also known as Khovanov-Lauda-Rouquier algebras or KLR-algebras) associated to Cartan data of finite type. The main result provides a classification of all cuspidal representations of a quiver Hecke algebra of finite type. The paper contains several rather technical parts where some representations are constructed and checked by brute force. At the same time, some constructions of the paper produce much “smaller” and easier results than the corresponding original constructions ofA. Kleshchev andA. Ram [Math. Ann. 349, No. 4, 943-975 (2011;Zbl 1267.20010)].

MSC:

20C08 Hecke algebras and their representations
17B37 Quantum groups (quantized enveloping algebras) and related deformations
05E10 Combinatorial aspects of representation theory
16G20 Representations of quivers and partially ordered sets

Citations:

Zbl 1267.20010

Cite

References:

[1]Arakawa, T.; Suzuki, T., Duality between \(s l_n(C)\) and the degenerate affine Hecke algebra of type \(A\), J. Algebra, 209, 288-304 (1998) ·Zbl 0919.17005
[2]Bernstein, I. N.; Zelevinsky, A. V., Induced representations of reductive \(p\)-adic groups, I, Ann. Sci. École Norm. Sup., 10, 441-472 (1977) ·Zbl 0412.22015
[3]Brundan, J.; Kleshchev, A., Hecke-Clifford Superalgebras, Crystals of Type \(A_{2 l}^{(2)}\) and Modular Branching Rules for \(\hat{S}_n\). Crystals of Type \(A_{2 l}^{(2)}\) and Modular Branching Rules for \(\hat{S}_n\), Represent. Theory, 5, 317-403 (2001) ·Zbl 1005.17010
[4]Brundan, J.; Kleshchev, A., Blocks of cyclotomic Hecke algebras and Khovanov-Lauda Algebras, Invent. Math., 178, 451-484 (2009) ·Zbl 1201.20004
[5]Green, J. A., Quantum groups, Hall algebras and quantum shuffles, Finite reductive groups (Luminy 1994). Finite reductive groups (Luminy 1994), Birkhäuser Prog. Math., 141, 273-290 (1997) ·Zbl 0890.17007
[6]Hill, D.; Kujawa, J.; Sussan, J., Affine Hecke-Clifford algebras and type \(Q\) Lie superalgebras, Math. Z., 268, 3-4, 1091-1158 (2011) ·Zbl 1231.20005
[7]Kashiwara, M., On crystal bases of the \(q\)-analogue of universal enveloping algebras, Duke Math. J., 63, 465-516 (1991) ·Zbl 0739.17005
[8]Khovanov, M.; Lauda, A., A diagrammatic approach to categorification of quantum groups I, Represent. Theory, 13, 309-347 (2009) ·Zbl 1188.81117
[9]Khovanov, M.; Lauda, A., A diagrammatic approach to categorification of quantum groups II, Trans. Amer. Math. Soc., 363, 2685-2700 (2011) ·Zbl 1214.81113
[10]Kleshchev, A.; Ram, A., Homogeneous representations of Khovanov-Lauda algebras, J. Eur. Math. Soc. (JEMS), 12, 5, 1293-1306 (2010) ·Zbl 1241.20005
[11]Kleshchev, A.; Ram, A., Representations of Khovanov-Lauda-Rouquier algebras and combinatorics of Lyndon words, Math. Ann., 349, 4, 943-975 (2011) ·Zbl 1267.20010
[12]Lalonde, P.; Ram, A., Standard Lyndon bases of Lie algebras and enveloping algebras, Trans. Amer. Math. Soc., 347, 1821-1830 (1995) ·Zbl 0833.17003
[13]Lauda, A.; Vazirani, M., Crystals from categorified quantum groups, Adv. in Math., 228, 2, 803-861 (2011) ·Zbl 1246.17017
[14]Leclerc, B., Dual canonical bases, quantum shuffles and \(q\)-characters, Math. Z., 246, 4, 691-732 (2004) ·Zbl 1052.17008
[15]Lusztig, G., Introduction to quantum groups, (Progress in Mathematics, vol. 110 (1993), Birkhäuser Boston Inc: Birkhäuser Boston Inc Boston, MA) ·Zbl 0304.58022
[16]Rosso, M., Groupes quantiques et algèbres de battage quantiques, C. R. Acad. Sci. Paris, 320, 145-148 (1995) ·Zbl 0929.17005
[17]Rosso, M., Quantum groups and quantum shuffles, Invent. Math., 133, 399-416 (1998) ·Zbl 0912.17005
[18]M. Rosso, Lyndon bases and the multiplicative formula for \(R\); M. Rosso, Lyndon bases and the multiplicative formula for \(R\)
[19]R. Rouquier, 2-Kac-Moody Algebras. arXiv:0812.5023; R. Rouquier, 2-Kac-Moody Algebras. arXiv:0812.5023 ·Zbl 1247.20002
[20]Zelevinsky, A., Induced representations of reductive \(p\)-adic groups II, Ann. Sci. E.N.S., 13, 165-210 (1980) ·Zbl 0441.22014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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