Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants
Neretin, Yurii A.
arXiv, 0012220 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-12-21
Classification:  Mathematics - Representation Theory,  Mathematical Physics,  Mathematics - Classical Analysis and ODEs,  Mathematics - Complex Variables,  Mathematics - Functional Analysis,  43A85, 22E46, 53C35, 32A25, 43A90, 33C05, 33E20, 15A15 
@article{0012220,
     author = {Neretin, Yurii A.},
     title = {Matrix balls, radial analysis of Berezin kernels, and hypergeometric
  determinants},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0012220}
}

Neretin, Yurii A. Matrix balls, radial analysis of Berezin kernels, and hypergeometric
  determinants. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0012220/