ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra
Name
S1088-4165-2018-00515-8.pdf
Description
Published version
Size
455.36 KB
Format
Adobe PDF
Checksum (MD5)
a7412382af9db85854c28037994eafa3
Author(s)
Lusztig, George
Yun, Zhiwei
Date Issued
2018
Journal
Representation Theory of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Version
Final published version
Abstract
© 2018 American Mathematical Society. In this paper we construct representations of certain graded double affine Hecke algebras (DAHA) with possibly unequal parameters from geometry. More precisely, starting with a simple Lie algebra g together with a ℤ/mℤ-grading ⊕i∈ℤ/mℤ gi and a block of DG0 (gi) as introduced in [J. Represent. Theory 21 (2017), pp. 277-321], we attach a graded DAHA and construct its action on the direct sum of spiral inductions in that block. This generalizes results of Vasserot [Duke Math J. 126 (2005), pp. 251-323] and Oblomkov- Yun [Adv. Math 292 (2016), pp. 601-706] which correspond to the case of the principal block.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1090/ERT/515
