$\mathbf {Z}/m$-graded Lie algebras and perverse sheaves, I
Authors:
George Lusztig and Zhiwei Yun
Journal:
Represent. Theory 21 (2017), 277-321
MSC (2010):
Primary 20G99
DOI:
https://doi.org/10.1090/ert/500
Published electronically:
September 14, 2017
Part II:
Represent. Theory 21 (2017), 322-353.
MathSciNet review:
3697026
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Abstract | References | Similar Articles | Additional Information
Abstract: We give a block decomposition of the equivariant derived category arising from a cyclically graded Lie algebra. This generalizes certain aspects of the generalized Springer correspondence to the graded setting.
- David Kazhdan and George Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987), no. 1, 153β215. MR 862716, DOI https://doi.org/10.1007/BF01389157
- Bertram Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81 (1959), 973β1032. MR 114875, DOI https://doi.org/10.2307/2372999
- G. Lusztig, Intersection cohomology complexes on a reductive group, Invent. Math. 75 (1984), no. 2, 205β272. MR 732546, DOI https://doi.org/10.1007/BF01388564
- George Lusztig, Character sheaves. I, Adv. in Math. 56 (1985), no. 3, 193β237. MR 792706, DOI https://doi.org/10.1016/0001-8708%2885%2990034-9
- George Lusztig, Character sheaves. II, III, Adv. in Math. 57 (1985), no. 3, 226β265, 266β315. MR 806210, DOI https://doi.org/10.1016/0001-8708%2885%2990064-7
- George Lusztig, Study of perverse sheaves arising from graded Lie algebras, Adv. Math. 112 (1995), no. 2, 147β217. MR 1327095, DOI https://doi.org/10.1006/aima.1995.1031
- L. Rider and A. Russell, Perverse sheaves on the nilpotent cone and Lusztigβs generalized Springer correspondence, arxiv:1409.7132.
- G. Lusztig, Study of antiorbital complexes, Representation theory and mathematical physics, Contemp. Math., vol. 557, Amer. Math. Soc., Providence, RI, 2011, pp. 259β287. MR 2848930, DOI https://doi.org/10.1090/conm/557/11036
- Robert Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I., 1968. MR 0230728
- Γ. B. Vinberg, The Weyl group of a graded Lie algebra, Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), no. 3, 488β526, 709 (Russian). MR 0430168
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Additional Information
George Lusztig
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Masssachusetts 02139
MR Author ID:
117100
Email:
gyuri@math.mit.edu
Zhiwei Yun
Affiliation:
Department of Mathematics, Yale University, New Haven, Connecticut 06511
MR Author ID:
862829
Email:
zhiweiyun@gmail.com
Received by editor(s):
October 12, 2016
Received by editor(s) in revised form:
June 23, 2017
Published electronically:
September 14, 2017
Additional Notes:
The first author was supported by NSF grant DMS-1566618.
The second author was supported by NSF grant DMS-1302071 and the Packard Foundation.
Article copyright:
© Copyright 2017
American Mathematical Society