Multivariate Jacobi polynomials and the Selberg integral. II

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 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.