Heisenberg parabolically induced representations of Hermitian Lie groups, Part II: Next-to-minimal representations and branching rules

Jan Frahm; Clemens Weiske; Genkai Zhang

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

Heisenberg parabolically induced representations of Hermitian Lie groups, Part II: Next-to-minimal representations and branching rules

Jan Frahm^*, Clemens Weiske, Genkai Zhang

^*Corresponding author af dette arbejde

Institut for Matematik

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

29 Downloads (Pure)

Abstract

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 $\operatorname{SO}_0(2,n)$ and $E_{6(-14)}$ we study some branching problems of these next-to-minimal representations.

Originalsprog	Engelsk
Titel	Symmetry in Geometry and Analysis, Volume 2 : Festschrift in Honor of Toshiyuki Kobayashi
Antal sider	30
Udgivelsessted	Singapore
Forlag	Birkhäuser Verlag
Publikationsdato	mar. 2025
Sider	197-226
Kapitel	6
ISBN (Trykt)	978-981-97-7661-0
ISBN (Elektronisk)	978-981-97-7662-7
DOI	https://doi.org/10.1007/978-981-97-7662-7_6
Status	Udgivet - mar. 2025

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

Emneord

math.RT

Adgang til dokumentet

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

2304.05663v1

Tjek tilgængelighed hos det Kgl. Bibliotek

Andre filer og links

Link to publication in Scopus

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

@inbook{12b18cd1eecb4cc18b18a543ca20bd7f,

title = "Heisenberg parabolically induced representations of Hermitian Lie groups, Part II: Next-to-minimal representations and branching rules",

abstract = "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 SO 0(2,n) and E 6(−14) we study some branching problems of these next-to-minimal representations.",

keywords = "math.RT",

author = "Jan Frahm and Clemens Weiske and Genkai Zhang",

note = "21 pages",

year = "2025",

month = mar,

doi = "10.1007/978-981-97-7662-7_6",

language = "English",

isbn = "978-981-97-7661-0",

series = "Progress in Mathematics",

publisher = "Birkh{\"a}user Verlag",

pages = "197--226",

booktitle = "Symmetry in Geometry and Analysis, Volume 2",

}

Frahm, J, Weiske, C & Zhang, G 2025, Heisenberg parabolically induced representations of Hermitian Lie groups, Part II: Next-to-minimal representations and branching rules. i Symmetry in Geometry and Analysis, Volume 2: Festschrift in Honor of Toshiyuki Kobayashi. Birkhäuser Verlag, Singapore, Progress in Mathematics, bind 358, s. 197-226. https://doi.org/10.1007/978-981-97-7662-7_6

Heisenberg parabolically induced representations of Hermitian Lie groups, Part II: Next-to-minimal representations and branching rules. / Frahm, Jan; Weiske, Clemens; Zhang, Genkai.
Symmetry in Geometry and Analysis, Volume 2: Festschrift in Honor of Toshiyuki Kobayashi. Singapore: Birkhäuser Verlag, 2025. s. 197-226 (Progress in Mathematics, Bind 358).

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

TY - CHAP

T1 - Heisenberg parabolically induced representations of Hermitian Lie groups, Part II

T2 - Next-to-minimal representations and branching rules

AU - Frahm, Jan

AU - Weiske, Clemens

AU - Zhang, Genkai

N1 - 21 pages

PY - 2025/3

Y1 - 2025/3

N2 - 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 SO 0(2,n) and E 6(−14) we study some branching problems of these next-to-minimal representations.

AB - 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 SO 0(2,n) and E 6(−14) we study some branching problems of these next-to-minimal representations.

KW - math.RT

UR - http://www.scopus.com/inward/record.url?scp=85218015159&partnerID=8YFLogxK

U2 - 10.1007/978-981-97-7662-7_6

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

M3 - Book chapter

SN - 978-981-97-7661-0

T3 - Progress in Mathematics

SP - 197

EP - 226

BT - Symmetry in Geometry and Analysis, Volume 2

PB - Birkhäuser Verlag

CY - Singapore

ER -

Frahm J, Weiske C, Zhang G. Heisenberg parabolically induced representations of Hermitian Lie groups, Part II: Next-to-minimal representations and branching rules. I Symmetry in Geometry and Analysis, Volume 2: Festschrift in Honor of Toshiyuki Kobayashi. Singapore: Birkhäuser Verlag. 2025. s. 197-226. (Progress in Mathematics, Bind 358). doi: 10.1007/978-981-97-7662-7_6

Heisenberg parabolically induced representations of Hermitian Lie groups, Part II: Next-to-minimal representations and branching rules

Abstract

Emneord

Adgang til dokumentet

Tjek tilgængelighed hos det Kgl. Bibliotek

Andre filer og links

Fingeraftryk

Projekter

Symmetry Breaking in Mathematics

Citationsformater