Representation rings of quantum groups

[摘要] Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings O(G(q)) of the classical groups, where q is transcendental. This is a ring theoretic formulation of the well-known fact that the representation theory of G(q) is completely analogous to its classical counterpart. The subalgebras of cocommutative elements in the corresponding FRT-bialgebras (defined by Faddeev, Reshetikhin, and Takhtadzhyan) are explicitly determined, using a bialgebra embedding of the FRT-bialgebra into the tensor product of the quantized coordinate ring and the one-variable polynomial ring. A parallel analysis of the subalgebras of adjoint coinvariants is carried out as well, yielding similar results with similar proofs. The basic adjoint coinvariants are interpreted as quantum traces of representations of the corresponding quantized universal enveloping algebra. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-01

[关键词] quantized function algebra;classical group;adjoint coaction;cocommutative element;quantum trace;FRT-bialgebra