Integrable modules over quantum symmetric pair coideal subalgebras

Abstract

We introduce the notion of integrable modules over $ı$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 $ı$quantum group. As an application, we show that the space of matrix coefficients of all simple integrable modules over an $ı$quantum group of finite type with specific parameters coincides with Bao-Song's coordinate ring of the $ı$quantum group.

Minor corrections. 22 pages, to appear in the Journal of the Institute of Mathematics of Jussieu

References in corpus (2)

• Canonical bases for tensor products and super Kazhdan-Lusztig theory
• Quasitriangular coideal subalgebras of $U_q(\mathfrak{g})$ in terms of generalized Satake diagrams