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

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

2006-10-29

arxiv.org/abs/math/0610896v2

Mathematics

Representation Theory

19 pages, some modifications made to the first version

Scientific paper

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.

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