Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants

Abstract

Consider the pseidounitary group $G=U(p,q)$ and its compact subgroup $K=U(p)$. We construct an explicit unitary intertwining operator from the tensor product of a holomorphic representation and a antiholomorphic representation of $G$ to the space $L^2(G/K)$. This implies the existense of a canonical action of the group $G\times G$ in $L^2(G/K)$. We also give a survey of analysis of Berezin kernels and their relations with special functions.

46 pages; misprints are corrected; addendum on pseudoriemannian symmetric spaces is added

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