Constructing irreducible representations of quantum groups $U_{q}(f_{m}(K))$

Xin Tang

paper

Constructing irreducible representations of quantum groups $U_{q} (f_{m} (K))$

arXiv:math/0610896

Abstract

In this paper, we construct families of irreducible representations for a class of quantum groups $U_{q} (f_{m} (K))$ . First, we give a natural construction of irreducible weight representations for $U_{q} (f_{m} (K))$ using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of $U_{q} (f_{m} (K))$ . As a result, the structure of Whittaker representations is determined, and all irreducible Whittaker representations are explicitly constructed. Finally, we prove that the annihilator of a Whittaker representation is centrally generated.

19 pages, some modifications made to the first version

Constructing irreducible representations of quantum groups Uq​(fm​(K))

Abstract

Constructing irreducible representations of quantum groups $U_{q} (f_{m} (K))$