a1 Department of Mathematics & Computer Science, Fayetteville State University, Fayetteville, NC 28301, USA (email: [email protected])
a2 Faculty of Mathematics & Computer Science, Hubei University, Wuhan 430062, People’s Republic of China (email: [email protected])
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.
(Received December 28 2007)
2000 Mathematics subject classification
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The second author was partially supported by NSFC, under grant 10501010.