Règles de branchement pour les groupes de Lie semi-simples et les noyaux reproduisants

Translated title of the contribution: Branching problems for semisimple Lie groups and reproducing kernels

Bent Ørsted, 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 these when restricted to a subgroup H of the same type by combining the classical results with the recent work of T. Kobayashi. We analyze aspects of having differential operators being symmetry-breaking operators; in particular, we prove in the so-called admissible case that every symmetry breaking (H-map) operator is a differential operator. We prove discrete decomposability under Harish-Chandra's condition of cusp form on the reproducing kernels. Our techniques are based on realizing discrete series representations as kernels of elliptic invariant differential operators.

Translated title of the contributionBranching problems for semisimple Lie groups and reproducing kernels
Original languageFrench
JournalComptes Rendus Mathematique
Volume357
Issue9
Pages (from-to)697-707
Number of pages11
ISSN1631-073X
DOIs
Publication statusPublished - Sept 2019

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