Advanced Studies in Pure Mathematics

Cells for a Hecke Algebra Representation

T. A. Springer

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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

Representation Theory of Algebraic Groups and Quantum Groups, T. Shoji, M. Kashiwara, N. Kawanaka, G. Lusztig and K. Shinoda, eds. (Tokyo: Mathematical Society of Japan, 2004), 469-482

Received: 18 February 2002
First available in Project Euclid: 3 January 2019

Permanent link to this document euclid.aspm/1546542395

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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.

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