## General Mathematics Colloquium

**20Apr2016**11:15 - 12:15

Speaker: Erik Koelink

Title: Matrix-valued orthogonal polynominals

### Abstract

Orthogonal polynomials form a classical part of mathematics and have many applications in mathematics, physics, etc. Classical examples are the Hermite, Laguerre, Gegenbauer, Jacobi polynomials. Matrix-valued orthogonal polynomials were introduced by M.G. Krein at the end of the 40ies. We discuss an explicit example of such a family of matrix-valued orthogonal polynomials, which is viewed as an analogue of the Gegenbauer polynomials. This family is obtained using shift operators, matrix-valued differential operators and Darboux factorisation. However, for this we require an initial case of matrix-valued orthogonal polynomials obtained using group theory and matrix-valued spherical functions, but we will focus on the elementary approach.

Location: KdVI meeting room, SP 105-107, F3.20.