Spherical functions and quantum groups

P. ROMÁN

Bogotá

Encuentro; Cuarto encuentro iberoameri- cano de polinomios ortogonales y sus aplicaciones; 2014

In this talk we will discuss the construction of families of matrix-valued orthogonal polynomials that arise naturally upon considering matrix-valued spherical functions on certain quantum groups. For the case of the quantum analog of the group SU(2)xSU(2), these polynomials are orthogonal with respect to a matrix weight that we can construct explicitly, and they solve a matrix-valued q-difference equation. Finally we will derive explicit expressions for the entries of the polynomials in terms of q-Racah and q-Ultraspherical polynomials.