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Hecke algebra representations related to spherical varieties

Authors: J. G. M. Mars and T. A. Springer
Journal: Represent. Theory 2 (1998), 33-69
MSC (1991): Primary 14M15, 55N33
Published electronically: February 11, 1998
MathSciNet review: 1600804
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Abstract: Let $G$ be a connected reductive group over the algebraic closure of a finite field and let $Y$ be a spherical variety for $G$. We consider perverse sheaves on $G$ and on $Y$ which have a weight for the action of a Borel subgroup $B$ and are endowed with an action of Frobenius. This leads to the definition of a ``generalized Hecke algebra'', attached to $G$, and of a module over that algebra, attached to $Y$. The same algebra and the same module can also be defined using constructible sheaves. Comparison of the two definitions gives, in the case of a symmetric variety $Y$ and $B$-equivariant sheaves, a geometric proof of results which Lusztig and Vogan obtained by representation theoretic means.

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Additional Information

J. G. M. Mars
Affiliation: Mathematisch Instituut, Universiteit Utrecht, Budapestlaan 6, 3508 TA Utrecht, Netherlands

T. A. Springer
Affiliation: Mathematisch Instituut, Universiteit Utrecht, Budapestlaan 6, 3508 TA Utrecht, Netherlands

Received by editor(s): April 17, 1997
Received by editor(s) in revised form: November 19, 1997
Published electronically: February 11, 1998
Article copyright: © Copyright 1998 American Mathematical Society

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