Representation theory, Hypergeometric Correlation Kernels,
and Random Matrices
I will report on a recent joint work with A. Borodin. Starting from a problem of noncommutative harmonic analysis we are led to new examples of random point ensembles, which are similar to those arising from spectra of random matrices. The correlations in our ensembles are described in terms of certain "integrable'' kernels on the line and on the one-dimensional lattice. These kernels are expressed through various special functions of hypergeometic type.