Thursday 14 January 2021, 12:45-13:15 via zoom
Erik Koelink (RU)
Special functions from group representations
There is an intimate connection between special functions and group representations. For compact groups this relates often to orthogonal polynomials, and we discuss a classical example related to \(SU(2)\) and Legendre polynomials in the framework of so-called Gelfand pairs. This concept is then extended to matrix valued spherical functions, which give rise to matrix valued orthogonal polynomials in several variables. This part will be introductory and focusing on an explicit example related to the compact group \(SU(n+1)\) of unitary \((n+1)\times (n+1)\) matrices of determinant \(1\). Most of the latter work described is joint with Maarten van Pruijssen en Pablo Román.