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

Xin Tang; Yunge Xu

paper

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

arXiv:math/0610895

Abstract

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.

Some minor modifications to the first version

On representations of quantum groups Uq​(fm​(K,H))

Abstract

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