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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.


A new basis for the representation ring of a Weyl group
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by G. Lusztig
Represent. Theory 23 (2019), 439-461
Published electronically: October 23, 2019


Let $W$ be a Weyl group. In this paper we define a new basis for the Grothendieck group of representations of $W$. This basis contains on the one hand the special representations of $W$ and on the other hand the representations of $W$ carried by the left cells of $W$. We show that the representations in the new basis have a certain bipositivity property.
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Bibliographic Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, Room 2-365, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Email:
  • Received by editor(s): January 1, 2400
  • Published electronically: October 23, 2019
  • Additional Notes: The author was supported by NSF grant DMS-1566618.
  • © Copyright 2019 American Mathematical Society
  • Journal: Represent. Theory 23 (2019), 439-461
  • MSC (2010): Primary 20G99
  • DOI:
  • MathSciNet review: 4021825