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ON REPRESENTATIONS OF QUANTUM GROUPS Uq(fm(K,H))

Part of: Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  01 October 2008

XIN TANG  and
YUNGE XU
XIN TANG*
Affiliation:
Department of Mathematics & Computer Science, Fayetteville State University, Fayetteville, NC 28301, USA (email: [email protected])
YUNGE XU
Affiliation:
Faculty of Mathematics & Computer Science, Hubei University, Wuhan 430062, People’s Republic of China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We construct families of irreducible representations for a class of quantum groups Uq(fm(K,H). First, we realize these quantum groups as hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for Uq(fm(K,H)). Second, we study the relationship between Uq(fm(K,H)) and Uq(fm(K)). As a result, any finite-dimensional weight representation of Uq(fm(K,H)) is proved to be completely reducible. Finally, we study the Whittaker model for the center of Uq(fm(K,H)), and a classification of all irreducible Whittaker representations of Uq(fm(K,H)) is obtained.

Keywords

hyperbolic algebrasspectral theoryWhittaker modelquantum groups

MSC classification

Secondary: 17B10: Representations, algebraic theory (weights) 17B35: Universal enveloping (super)algebras 17B37: Quantum groups (quantized enveloping algebras) and related deformations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 261 - 284
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The second author was partially supported by NSFC, under grant 10501010.

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