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Representations of the twisted SU(2) quantum group and some q- hypergeometric orthogonal polynomials. (English) Zbl 0681.22020

Author’s summary: The matrix elements of the irreducible unitary representations of the twisted SU(2) quantum group are computed explicitly. It is shown that they can be identified with two different classes of q-hypergeometric orthogonal polynomials: with the little q- Jacobi polynomials and with certain q-analogues of Krawtchouk polynomials. The orthogonality relations for these polynomials correspond to Schur type orthogonality relations in the first case and to the unitarity conditions for the representations in the second case. The paper also contains a new proof of Woronowicz’ classification of the unitary irreducible representations of this quantum group. It avoids infinitesimal methods. Symmetries of the matrix elements of the irreducible unitary representations are proved without using the explicit expressions.
Reviewer: A.Guts

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
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