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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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Hecke algebra representations related to spherical varieties
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by J. G. M. Mars and T. A. Springer
Represent. Theory 2 (1998), 33-69
Published electronically: February 11, 1998


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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Bibliographic 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
  • © Copyright 1998 American Mathematical Society
  • Journal: Represent. Theory 2 (1998), 33-69
  • MSC (1991): Primary 14M15, 55N33
  • DOI:
  • MathSciNet review: 1600804