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

TY - JOUR

T1 - Règles de branchement pour les groupes de Lie semi-simples et les noyaux reproduisants

AU - Ørsted, Bent

AU - Vargas, Jorge A.

PY - 2019/9

Y1 - 2019/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85072707911&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2019.09.004

DO - 10.1016/j.crma.2019.09.004

M3 - Tidsskriftartikel

AN - SCOPUS:85072707911

SN - 1631-073X

VL - 357

SP - 697

EP - 707

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9

ER -