Construct irreducible representations of quantum groups Uq(ƒm(K))

Xin Tang

doi:10.1007/s11464-008-0027-8

Front. Math. China ›› 2008, Vol. 3 ›› Issue (3) : 371 -397. DOI: 10.1007/s11464-008-0027-8

Research Article

Construct irreducible representations of quantum groups U_q(ƒ_m(K))

Xin Tang ¹^,^a

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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.

Keywords

Hyperbolic algebra / spectral theory / Whittaker modules / quantum group

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Xin Tang. Construct irreducible representations of quantum groups U_q(ƒ_m(K)). Front. Math. China, 2008, 3(3): 371-397 DOI:10.1007/s11464-008-0027-8

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