Branching problems in reproducing kernel spaces
Representation Theory
2020-12-23 v3
Abstract
For a semisimple Lie group satisfying the equal rank condition, the most basic family of unitary irreducible representations is the discrete series found by Harish-Chandra. In this paper, we study some of the branching laws for discrete series when restricted to a subgroup of the same type by combining classical results with recent work of T. Kobayashi; in particular, we prove discrete decomposability under Harish-Chandra's condition of cusp form on the reproducing kernel. We show a relation between discrete decomposability and representing certain intertwining operators in terms of differential operators.
Keywords
Cite
@article{arxiv.1906.08119,
title = {Branching problems in reproducing kernel spaces},
author = {Bent Orsted and Jorge A. Vargas},
journal= {arXiv preprint arXiv:1906.08119},
year = {2020}
}