Finite dimensional representations of Uq(C(n+1)) at arbitrary q
Abstract
A method is developed to construct irreducible representations(irreps) of the quantum supergroup Uq(C(n+1)) in a systematic fashion. It is shown that every finite dimensional irrep of this quantum supergroup at generic q is a deformation of a finite dimensional irrep of its underlying Lie superalgebra C(n+1), and is essentially uniquely characterized by a highest weight. The character of the irrep is given. When q is a root of unity, all irreps of Uq(C(n+1)) are finite dimensional; multiply atypical highest weight irreps and (semi)cyclic irreps also exist. As examples, all the highest weight and (semi)cyclic irreps of Uq(C(2)) are thoroughly studied.
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