## 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.## References

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## Bibliographic Information

**Gail Letzter**- Affiliation: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
- MR Author ID: 228201
- Email: letzter@math.vt.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Represent. Theory
**4**(2000), 64-96 - MSC (2000): Primary 17B37
- DOI: https://doi.org/10.1090/S1088-4165-00-00087-X
- MathSciNet review: 1742961