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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.


Stability of $\imath$canonical bases of irreducible finite type of real rank one
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by Hideya Watanabe PDF
Represent. Theory 27 (2023), 1-29 Request permission


It has been known since their birth in Bao and Wang’s work that the $\imath$canonical bases of $\imath$quantum groups are not stable in general. In the author’s previous work, the stability of $\imath$canonical bases of certain quasi-split types turned out to be closely related to the theory of $\imath$crystals. In this paper, we prove the stability of $\imath$canonical bases of irreducible finite type of real rank $1$, for which the theory of $\imath$crystals has not been developed, by means of global and local crystal bases.
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Additional Information
  • Hideya Watanabe
  • Affiliation: Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University, Osaka 558-8585, Japan
  • MR Author ID: 1196919
  • ORCID: 0000-0002-7705-8783
  • Email:
  • Received by editor(s): July 17, 2022
  • Received by editor(s) in revised form: November 12, 2022, and December 19, 2022
  • Published electronically: March 6, 2023
  • Additional Notes: This work was supported by JSPS KAKENHI Grant Numbers JP20K14286 and JP21J00013.
  • © Copyright 2023 American Mathematical Society
  • Journal: Represent. Theory 27 (2023), 1-29
  • MSC (2020): Primary 17B37; Secondary 17B10
  • DOI: