Separation of spectra in analysis of Berezin kernels
Representation Theory
2013-01-15 v1 Mathematical Physics
math.MP
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 one-type 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.
Keywords
Cite
@article{arxiv.math/9906075,
title = {Separation of spectra in analysis of Berezin kernels},
author = {Yu. A. Neretin},
journal= {arXiv preprint arXiv:math/9906075},
year = {2013}
}