On representations of quantum groups $U_{q}(f_{m}(K,H))$

Details On representations of quantum groups $U_{q}(f_{m}(K,H))$ On representations of quantum groups $U_{q}(f_{m}(K,H))$

2006-10-29

arxiv.org/abs/math/0610895v2

Mathematics

Representation Theory

Some minor modifications to the first version

Scientific paper

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

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