Harish-Chandra modules for quantum symmetric pairs

Letzter, Gail

doi:10.1090/S1088-4165-00-00087-X

Harish-Chandra modules for quantum symmetric pairs
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by Gail Letzter

Represent. Theory 4 (2000), 64-96

DOI: https://doi.org/10.1090/S1088-4165-00-00087-X

Published electronically: February 18, 2000

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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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