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Construct irreducible representations of quantum
groups (()) |
| TANG Xin |
| Department of Mathematics & Computer Science, Fayetteville State University |
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Abstract In this paper, we construct families of irreducible representations for a class of quantum groups Uq(fm(K)). First, we give a natural construction of irreducible weight representations for Uq(fm(K)) using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of Uq(fm(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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Issue Date: 05 September 2008
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