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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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Harish-Chandra modules for quantum symmetric pairs
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by Gail Letzter PDF
Represent. Theory 4 (2000), 64-96 Request permission

Abstract:

Let $U$ denote the quantized enveloping algebra associated to a semisimple Lie algebra. This paper studies Harish-Chandra modules for the recently constructed quantum symmetric pairs $U$,$B$ in the maximally split case. Finite-dimensional $U$-modules are shown to be Harish-Chandra as well as the $B$-unitary socle of an arbitrary module. A classification of finite-dimensional spherical modules analogous to the classical case is obtained. A one-to-one correspondence between a large class of natural finite-dimensional simple $B$-modules and their classical counterparts is established up to the action of almost $B$-invariant elements.
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Additional Information
  • Gail Letzter
  • Affiliation: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
  • MR Author ID: 228201
  • Email: letzter@math.vt.edu
  • Received by editor(s): October 22, 1999
  • Received by editor(s) in revised form: November 19, 1999
  • Published electronically: February 18, 2000
  • Additional Notes: The author was supported by NSF grant no. DMS-9753211
  • © Copyright 2000 American Mathematical Society
  • Journal: Represent. Theory 4 (2000), 64-96
  • MSC (2000): Primary 17B37
  • DOI: https://doi.org/10.1090/S1088-4165-00-00087-X
  • MathSciNet review: 1742961