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Finite dimensional representations of $U_q(C(n+1))$ at arbitrary $q$ | | R. B. Zhang
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7 Jun 1993 | | Journal: | J.Phys. A26 (1993) 7041-7060 | | Subject: | High Energy Physics - Theory; Quantum Algebra | hep-th math.QA | | Abstract: | 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. | | Source: | arXiv, hep-th/9306036 | | Services: | Forum | Review | PDF | Favorites | |
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