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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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A new basis for the representation ring of a Weyl group
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by G. Lusztig PDF
Represent. Theory 23 (2019), 439-461 Request permission

Abstract:

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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Additional Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, Room 2-365, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Email: gyuri@mit.edu
  • 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: https://doi.org/10.1090/ert/534
  • MathSciNet review: 4021825