Matrix Valued Orthogonal Polynomials related to (SU(2) x SU(2),diag)

P. ROMÁN

Decin

Congreso; Special Functions and Orthogonal Polynomials of Lie Groups and their Applications, Decin, República Checa; 2011

We study the matrix-valued spherical functions for the pair (K x K, K), K=SU(2). By restriction to the subgroup A the matrix-valued spherical functions are diagonal. For suitable set of representations we take these diagonals into a matrix-valued function, which are the full spherical functions. Their orthogonality is a consequence of the Schur orthogonality relations. From the full spherical functions we obtain matrix-valued orthogonal polynomials of arbitrary size, and they satisfy a three-term recurrence relation which follows by considering tensor product decompositions. An explicit expression for the weight and the complete block-diagonalization of the matrix-valued orthogonal polynomials is obtained.