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

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 p-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.