Construct irreducible representations of quantum groups U
q
(?
m
(K)) |
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Authors: | Xin Tang |
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Institution: | (1) Department of Mathematics & Computer Science, Fayetteville State University, Fayetteville, NC 28301, USA |
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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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Keywords: | Hyperbolic algebra spectral theory Whittaker modules quantum group |
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