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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.


Cartan subalgebras for quantum symmetric pair coideals
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by Gail Letzter
Represent. Theory 23 (2019), 88-153
Published electronically: January 31, 2019


There is renewed interest in the coideal subalgebras used to form quantum symmetric pairs because of recent discoveries showing that they play a fundamental role in the representation theory of quantized enveloping algebras. However, there is still no general theory of finite-dimensional modules for these coideals. In this paper, we establish an important step in this direction: we show that every quantum symmetric pair coideal subalgebra admits a quantum Cartan subalgebra which is a polynomial ring that specializes to its classical counterpart. The construction builds on Kostant and Sugiura’s classification of Cartan subalgebras for real semisimple Lie algebras via strongly orthogonal systems of positive roots. We show that these quantum Cartan subalgebras act semisimply on finite-dimensional unitary modules and identify particularly nice generators of the quantum Cartan subalgebra for a family of examples.
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Bibliographic Information
  • Gail Letzter
  • Affiliation: Mathematics Research Group, National Security Agency, Fort Meade, Maryland 20755-6844
  • MR Author ID: 228201
  • Email:
  • Received by editor(s): June 4, 2017
  • Received by editor(s) in revised form: November 23, 2018
  • Published electronically: January 31, 2019
  • © Copyright 2019 American Mathematical Society
  • Journal: Represent. Theory 23 (2019), 88-153
  • MSC (2010): Primary 17B37; Secondary 17B10, 17B22
  • DOI:
  • MathSciNet review: 3904162