Quasisplit Hecke algebras and symmetric spaces
Author(s)Lusztig, George; Vogan, David A.
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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 [bar over O] of O, the multiplicity space of L' in a cohomology sheaf of the intersection cohomology of [bar over 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Duke Mathematical Journal
Duke University Press
Lusztig, George, and David A. Vogan Jr. “Quasisplit Hecke Algebras and Symmetric Spaces.” Duke Mathematical Journal 163, no. 5 (April 2014): 983–1034.
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