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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.


From Weyl groups to semisimple groups
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by G. Lusztig PDF
Represent. Theory 27 (2023), 51-61 Request permission


In this paper we show, using ideas from the theory of total positivity, how a number of properties of a semisimple group over the complex numbers can be presented purely in terms of the Weyl group. We also describe some new connections of the theory of canonical bases with total positivity.
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Additional Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Received by editor(s): January 23, 2022
  • Received by editor(s) in revised form: November 19, 2022, and December 13, 2022
  • Published electronically: March 21, 2023
  • Additional Notes: The author was supported by NSF grant DMS-1855773 and by a Simons Fellowship
  • © Copyright 2023 American Mathematical Society
  • Journal: Represent. Theory 27 (2023), 51-61
  • MSC (2020): Primary 20G05
  • DOI: