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INTEGRABLE MODULES OVER QUANTUM SYMMETRIC PAIR COIDEAL SUBALGEBRAS

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  05 June 2025

Hideya Watanabe Open the ORCID record for Hideya Watanabe [Opens in a new window]
Hideya Watanabe*
Affiliation:
College of Science, Rikkyo University , 3-34-1, Nishi-Ikebukuro, Toshima-ku, Tokyo, 171-8501, Japan
*
(watanabehideya@gmail.com)
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Abstract

We introduce the notion of integrable modules over $\imath $quantum groups (a.k.a. quantum symmetric pair coideal subalgebras). After determining a presentation of such modules, we prove that each integrable module over a quantum group is integrable when restricted to an $\imath $quantum group. As an application, we show that the space of matrix coefficients of all simple integrable modules over an $\imath $quantum group of finite type with specific parameters coincides with Bao-Song’s coordinate ring of the $\imath $quantum group.

Keywords

quantum symmetric pairrepresentation theoryintegrable modulecanonical basis

MSC classification

Primary: 17B10: Representations, algebraic theory (weights)
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 24 , Issue 6 , November 2025 , pp. 2257 - 2282
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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