Separation of spectra in analysis of Berezin kernels
Abstract
Consider an unitary highest weight representation of a group U(p,q) in holomorphic functions on the symmetric space U(p,q)/U(p)\times U(q). Consider its restriction \rho to the subgroup O(p,q). This restriction has a complicated spectrum consisting of representations having different types. We construct a decomposition of \rho to a finite direct sum of representations \tau_j such that each summand \tau_j has spectrum consisting of onetype representations. Our tool is theorems about restrictions of holomorphic functions on Cartan domain U(p,q)/U(p)\times U(q) to submanifolds of the boundary. We also obtain Plancherel formula for this restriction.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1999
 arXiv:
 arXiv:math/9906075
 Bibcode:
 1999math......6075N
 Keywords:

 Mathematics  Representation Theory;
 Mathematical Physics
 EPrint:
 Functional Analysis and Its Applications, 2000, 34:3, 197207