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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Hecke modules based on involutions in extended Weyl groups
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by G. Lusztig
Represent. Theory 22 (2018), 246-277
Published electronically: December 20, 2018


Let $X$ be the group of weights of a maximal torus of a simply connected semisimple group over $\mathbf {C}$ and let $W$ be the Weyl group. The semidirect product $W((\mathbf {Q}\otimes X)/X)$ is called an extended Weyl group. There is a natural $\mathbf {C}(v)$-algebra $\mathbf {H}$ called the extended Hecke algebra with basis indexed by the extended Weyl group which contains the usual Hecke algebra as a subalgebra. We construct an $\mathbf {H}$-module with basis indexed by the involutions in the extended Weyl group. This generalizes a construction of the author and Vogan.
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Bibliographic Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Email:
  • Received by editor(s): November 8, 2017
  • Received by editor(s) in revised form: October 5, 2018
  • Published electronically: December 20, 2018
  • Additional Notes: This research was supported by NSF grant DMS-1566618.
  • © Copyright 2018 American Mathematical Society
  • Journal: Represent. Theory 22 (2018), 246-277
  • MSC (2010): Primary 20G99, 33D80
  • DOI:
  • MathSciNet review: 3892873