## Advanced Studies in Pure Mathematics

### Cells for a Hecke Algebra Representation

T. A. Springer

#### 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 $W$.

#### Article information

Dates
First available in Project Euclid: 3 January 2019

https://projecteuclid.org/ euclid.aspm/1546542395

Digital Object Identifier
doi:10.2969/aspm/04010469

Mathematical Reviews number (MathSciNet)
MR2074602

Zentralblatt MATH identifier
1101.14059

#### Citation

Springer, T. A. Cells for a Hecke Algebra Representation. Representation Theory of Algebraic Groups and Quantum Groups, 469--482, Mathematical Society of Japan, Tokyo, Japan, 2004. doi:10.2969/aspm/04010469. https://projecteuclid.org/euclid.aspm/1546542395