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

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

2000-12-21

arxiv.org/abs/math/0012220v2

Mathematics

Representation Theory

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

Scientific paper

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.

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