Hiroyuki Ochiai
Nagoya University, Japan
Title: Hypergeometric functions in representation theory

The classical (Gauss) hypergeometric function is a special function with a series expansion, satisfies a linear differential equation, and has an integral representation. It arises in the representation theory of SL(2,R) as a spherical function, and also on the Grassmannian manifold G(2,4). In this lecture, we start with several connection between Gauss hypergeometric functions and functions on homogeneous spaces. We will go into a generalization to multivariable hypergeometric functions and higher rank semisimple Lie groups. No knowledge on special functions is assumed