Finite dimensional representations of $U_q(C(n+1))$ at arbitrary $q$

Details Finite dimensional representations of $U_q(C(n+1))$ at arbitrary $q$ Finite dimensional representations of $U_q(C(n+1))$ at arbitrary $q$

1993-06-07

arxiv.org/abs/hep-th/9306036v1

J.Phys. A26 (1993) 7041-7060

Physics

High Energy Physics

High Energy Physics - Theory

21 pages

Scientific paper

10.1088/0305-4470/26/23/042

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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