Matrix-valued orthogonal polynomials related to the quantum analog of SU(2)xSU(2)

PABLO ROMÁN

Liege

Encuentro; IAP Dygest Annual meeting; 2014

University of Liege

Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU(2)xSU(2),diag SU(2)) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantized universal enveloping algebra with a coideal subalgebra. The matrix-valued spherical functions give rise to matrix-valued orthogonal polynomials, which are matrix-valued analogues of a subfamily of Askey-Wilson polynomials. For these matrix-valued orthogonal polynomials a number of properties are derived using this quantum group interpretation, such as the orthogonality relations from the Schur orthogonality relations, the three-term recurrence relation and the structure of the weight matrix in terms Chebyshev polynomials from tensor product decompositions, the matrix-valued Askey-Wilson type q-difference operators from the Casimir elements.