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Representation Theory

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Harish-Chandra modules for quantum symmetric pairs

Author: Gail Letzter
Journal: Represent. Theory 4 (2000), 64-96
MSC (2000): Primary 17B37
Published electronically: February 18, 2000
MathSciNet review: 1742961
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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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Additional Information

Gail Letzter
Affiliation: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

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
Article copyright: © Copyright 2000 American Mathematical Society

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