Quasisplit Hecke algebras and symmetric spaces
Name
Lusztig_Quasisplit hecke.pdf
Size
412.87 KB
Format
Adobe PDF
Checksum (MD5)
b1443b9f51de76eb6776e7cceea610ff
Author(s)
Lusztig, George
Vogan, David A.
Date Issued
March 2014
Journal
Duke Mathematical Journal
Publisher
Duke University Press
Citation
Lusztig, George, and David A. Vogan Jr. “Quasisplit Hecke Algebras and Symmetric Spaces.” Duke Mathematical Journal 163, no. 5 (April 2014): 983–1034.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1215/00127094-2644684
