Restricting holomorphic discrete series representations to a compact dual pair

Jan Frahm; Quentin Labriet

doi:10.1007/978-981-97-7662-7_4

Restricting holomorphic discrete series representations to a compact dual pair

Jan Frahm, Quentin Labriet

Institut for Matematik

Publikation: Bidrag til bog/antologi/rapport/proceeding › Bidrag til bog/antologi › Forskning › peer review

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Abstract

The goal of this article is to study the branching problem for a holomorphic discrete series representation of the conformal group of a simple Euclidean Jordan algebra $V$ restricted to the subgroup $\operatorname{PSL}_2(\mathbb{R})\times\operatorname{Aut}(V)$ where $\operatorname{Aut}(V)$ denotes the compact group of automorphisms of $V$. We use a realization of the holomorphic discrete series on a space of vector-values $L^2$-functions as well as the stratified model developed by the second author to relate the branching problem to the decomposition of certain representations of the compact group $\operatorname{Aut}(V)$ and to vector-valued orthogonal polynomials.

Originalsprog	Engelsk
Titel	Symmetry in Analysis and Geometry : Festschrift in Honor of Toshiyuki Kobayashi
Redaktører	Michael Pevzner, Hideko Sekiguchi
Antal sider	19
Vol/bind	2
Forlag	Birkhäuser Verlag
Publikationsdato	mar. 2025
Sider	95-113
Kapitel	4
DOI	https://doi.org/10.1007/978-981-97-7662-7_4
Status	Udgivet - mar. 2025

Navn	Progress in Mathematics
Vol/bind	358
ISSN	0743-1643

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10.1007/978-981-97-7662-7_4

2303.17991v1

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Symmetry Breaking in Mathematics
Frahm, J. (PI), Weiske, C. (Deltager), Ditlevsen, J. (Deltager), Spilioti, P. (Deltager), Bang-Jensen, F. J. (Deltager) & Labriet, Q. (Deltager)
01/08/2019 → 31/07/2024
Projekter: Projekt › Forskning

Citationsformater

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Restricting holomorphic discrete series representations to a compact dual pair. / Frahm, Jan; Labriet, Quentin.
Symmetry in Analysis and Geometry: Festschrift in Honor of Toshiyuki Kobayashi. red. / Michael Pevzner; Hideko Sekiguchi. Bind 2 Birkhäuser Verlag, 2025. s. 95-113 (Progress in Mathematics, Bind 358).

Publikation: Bidrag til bog/antologi/rapport/proceeding › Bidrag til bog/antologi › Forskning › peer review

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Restricting holomorphic discrete series representations to a compact dual pair

Abstract

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Symmetry Breaking in Mathematics

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