67 research outputs found
Representation rings of quantum groups
Generators and relations are given for the subalgebra of cocommutative
elements in the quantized coordinate rings of the classical groups, where the
deformation parameter q is transcendental. This is a ring theoretic formulation
of the well known fact that the representation theory of the quantized group 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.Comment: 29 page
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