Cuspidal local systems and graded Hecke algebras. I
type: Item
instance of: scholarly article
title: Cuspidal local systems and graded Hecke algebras. I
zbMATH Open document ID: 0699.22026
DOI: 10.1007/BF02699129
author: G. Lusztig
published in: Publications Mathématiques
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104030
review text: Hecke algebras of affine Weyl groups with equal parameters are important to representation theory of p-adic reductive groups because their simple modules give those representations that admit an Iwahori fixed vector. But also Hecke algebras with unequal parameters occur in representation theory, i.e. as endomorphism algebras of induced representations. The paper is concerned with the graded version of H of such an algebra with respect to a natural filtration. Similar to [\textit{D. Kazhdan}, \textit{G. Lusztig}, Invent. Math. 87, 153-215 (1987; Zbl 0613.22004)] where affine Hecke algebras are treated, the algebra H is realized in equivariant homology of a generalized flag variety of G, where G is the complex Lie group attached to the root data defining H. Thus the simple H-modules are classified in a way similar to [loc. cit.].
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 14C35
zbMATH DE Number: 4146302
zbMATH Keywords: Hecke algebras
zbMATH Keywords: affine Weyl groups
zbMATH Keywords: p-adic reductive groups
zbMATH Keywords: simple modules
zbMATH Keywords: equivariant homology
zbMATH Keywords: generalized flag variety
zbMATH Keywords: root data
reviewed by: Anton Deitmar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4146302