Cells for a Hecke Algebra Representation

Abstract

If $Y$ is an affine symmetric variety for the reductive group $G$ with Weyl group $W$, there exists by Lusztig and Vogan a representation of the Hecke algebra of $W$ in a module which has a basis indexed by the set $\Lambda$ of pairs $(v, \xi)$, where $v$ is an orbit in $Y$ of a Borel group $B$ and $\xi$ is a $B$-equivariant rank one local system on $v$. We introduce cells in $\Lambda$ and associate with a cell a two-sided cell in $W$.