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arXiv · 1906.08119

Branching problems in reproducing kernel spaces

Bent Orsted·Jorge A. Vargas
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Abstract

For a semisimple Lie group $G$ 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 $H$ 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.

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BibTeXRIS

Bent Orsted, Jorge A. Vargas. 2019-06-19. Branching problems in reproducing kernel spaces. https://doi.org/10.1215/00127094-2020-0032

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