1 April 2014 Quasisplit Hecke algebras and symmetric spaces
George Lusztig, David A. Vogan Jr.
Duke Math. J. 163(5): 983-1034 (1 April 2014). DOI: 10.1215/00127094-2644684


Let (G,K) be a symmetric pair over an algebraically closed field of characteristic different from 2, and let σ be an automorphism with square 1 of G preserving K. In this paper we consider the set of pairs (O,L) where O is a σ-stable K-orbit on the flag manifold of G and L is an irreducible K-equivariant local system on O which is “fixed” by σ. Given two such pairs (O,L), (O',L'), with O' in the closure O¯ of O, the multiplicity space of L' in a cohomology sheaf of the intersection cohomology of O¯ with coefficients in L (restricted to O') carries an involution induced by σ, and we are interested in computing the dimensions of its +1 and 1 eigenspaces. We show that this computation can be done in terms of a certain module structure over a quasisplit Hecke algebra on a space spanned by the pairs (O,L) as above.


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George Lusztig. David A. Vogan Jr.. "Quasisplit Hecke algebras and symmetric spaces." Duke Math. J. 163 (5) 983 - 1034, 1 April 2014. https://doi.org/10.1215/00127094-2644684


Published: 1 April 2014
First available in Project Euclid: 26 March 2014

zbMATH: 1300.20006
MathSciNet: MR3189436
Digital Object Identifier: 10.1215/00127094-2644684

Primary: 20G40
Secondary: 20C08

Rights: Copyright © 2014 Duke University Press

Vol.163 • No. 5 • 1 April 2014
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