Nonsplit Hecke algebras and perverse sheaves
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1501.07588.pdf
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326.1 KB
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Author(s)
Lusztig, George
Date Issued
October 2016
Journal
Selecta Mathematica
Publisher
Springer-Verlag
Citation
Lusztig, G. “Nonsplit Hecke Algebras and Perverse Sheaves.” Selecta Mathematica 22, 4 (October 2016): 1953–1986 © 2016 Springer International Publishing
Version
Original manuscript
Abstract
Let H be a Hecke algebra arising as an endomorphism algebra of the representation of a Chevalley group G over induced by a unipotent cuspidal representation of a Levi quotient L of a parabolic subgroup. We assume that L is not a torus. In this paper we outline a geometric interpretation of the coefficients of the canonical basis of H in terms of perverse sheaves. We illustrate this in detail in the case where the Weyl group of G is ot type and that of L is of type. Keywords: Hecke algebra; Parabolic character sheaf; Canonical basis
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/S00029-016-0272-8
