Heisenberg Parabolically Induced Representations of Hermitian Lie Groups, Part II: Next-to-Minimal Representations and Branching Rules
Kapitel i bok, 2025

Every simple Hermitian Lie group has a unique family of spherical representations induced from a maximal parabolic subgroup whose unipotent radical is a Heisenberg group. For most Hermitian groups, this family contains a complementary series, and at its endpoint sits a proper unitarizable subrepresentation. We show that this subrepresentation is next-to-minimal in the sense that its associated variety is a next-to-minimal nilpotent coadjoint orbit. Moreover, for the Hermitian groups SO0(2,n) and E6(−14) we study some branching problems of these next-to-minimal representations.

Författare

Jan Frahm

Aarhus Universitet

Clemens Weiske

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Genkai Zhang

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Progress in Mathematics

0743-1643 (ISSN) 2296-505X (eISSN)

Vol. 358 197-226

Representationer av Liegrupper. Harmonisk och komplex analys på symmetriska och lokalt symmetriska rum

Vetenskapsrådet (VR), 2019-01-01 -- 2022-12-31.

Vetenskapsrådet (VR) (2022-02861), 2023-01-01 -- 2026-12-31.

Ämneskategorier (SSIF 2025)

Algebra och logik

DOI

10.1007/978-981-97-7662-7_6

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Senast uppdaterat

2025-03-25