Multivariate Jacobi Polynomials and the Selberg Integral. II

Abstract

The problem of harmonic analysis for infinite-dimensional classical groups and symmetric spaces leads to a family of probability measures with infinite-dimensional support. In the present paper, we construct these measures in a different way, which makes it possible to substantially extend the range of the parameters. The measures that we obtain can be interpreted as the result of a formal analytic continuation of the N-dimensional beta distributions which appear in the Selberg integral. Our procedure of analytic continuation, based on Carlson’s theorem, turns N into a complex parameter. Bibliography: 20 titles.