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Construct irreducible representations of quantum groups U q (ƒ m (K))

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Abstract

In this paper, we construct families of irreducible representations for a class of quantum groups U q (ƒ m (K)). First, we give a natural construction of irreducible weight representations for U q (ƒ m (K)) using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of U q (ƒ 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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  1. Department of Mathematics & Computer Science, Fayetteville State University, Fayetteville, NC, 28301, USA

    Xin Tang

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  1. Xin Tang
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Correspondence to Xin Tang.

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Tang, X. Construct irreducible representations of quantum groups U q (ƒ m (K)). Front. Math. China 3, 371–397 (2008). https://doi.org/10.1007/s11464-008-0027-8

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  • DOI: https://doi.org/10.1007/s11464-008-0027-8

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