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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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Global crystal bases for integrable modules over a quantum symmetric pair of type AIII
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by Hideya Watanabe PDF
Represent. Theory 25 (2021), 27-66 Request permission


In this paper, we study basic properties of global $\jmath$-crystal bases for integrable modules over a quantum symmetric pair coideal subalgebra $\mathbf {U}^{\jmath }$ associated to the Satake diagram of type AIII without black nodes. Also, we obtain an intrinsic characterization of the $\jmath$-crystal bases, whose original definition is artificial.
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Additional Information
  • Hideya Watanabe
  • Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8052, Japan
  • MR Author ID: 1196919
  • ORCID: 0000-0002-7705-8783
  • Email:
  • Received by editor(s): November 16, 2019
  • Received by editor(s) in revised form: September 21, 2020
  • Published electronically: January 12, 2021
  • Additional Notes: This work was supported by JSPS KAKENHI grant number 17J00172
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 27-66
  • MSC (2020): Primary 17B10
  • DOI:
  • MathSciNet review: 4198491