Duke Mathematical Journal
- Duke Math. J.
- Volume 163, Number 5 (2014), 983-1034.
Quasisplit Hecke algebras and symmetric spaces
Let be a symmetric pair over an algebraically closed field of characteristic different from , and let be an automorphism with square of preserving . In this paper we consider the set of pairs where is a -stable -orbit on the flag manifold of and is an irreducible -equivariant local system on which is “fixed” by . Given two such pairs , , with in the closure of , the multiplicity space of in a cohomology sheaf of the intersection cohomology of with coefficients in (restricted to ) carries an involution induced by , and we are interested in computing the dimensions of its and 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 as above.
Duke Math. J., Volume 163, Number 5 (2014), 983-1034.
First available in Project Euclid: 26 March 2014
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Lusztig, George; Vogan Jr., David A. Quasisplit Hecke algebras and symmetric spaces. Duke Math. J. 163 (2014), no. 5, 983--1034. doi:10.1215/00127094-2644684. https://projecteuclid.org/euclid.dmj/1395856221