Branching problems in reproducing kernel spaces

TY - JOUR

T1 - Branching problems in reproducing kernel spaces

AU - Ørsted, Bent

AU - Vargas, Jorge A.

N1 - Publisher Copyright: © 2020 Duke University Press. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

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 our work here 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 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.

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 our work here 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 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.

UR - http://www.scopus.com/inward/record.url?scp=85098330050&partnerID=8YFLogxK

U2 - 10.1215/00127094-2020-0032

DO - 10.1215/00127094-2020-0032

M3 - Journal article

AN - SCOPUS:85098330050

SN - 0012-7094

VL - 169

SP - 3477

EP - 3537

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 18

ER -