/ 93 06 03 6 v 1 7 J un 1 99 3 Finite Dimensional Representations of U q ( C ( n + 1 ) ) at Arbitrary q
نویسنده
چکیده
A method is developed to construct irreducible representations(irreps) of the quantum supergroup U q (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 U q (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 U q (C(2)) are thoroughly studied.
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