Graded hypoellipticity of BGG sequences

Shantanu Dave; Stefan Haller

doi:10.1007/s10455-022-09870-0

Graded hypoellipticity of BGG sequences

Shantanu Dave, Stefan Haller (Korresp. Autor*in)

Institut für Mathematik

Veröffentlichungen: Beitrag in Fachzeitschrift › Artikel › Peer Reviewed

Abstract

This article studies hypoellipticity on general filtered manifolds. We extend the Rockland
criterion to a pseudodifferential calculus on filtered manifolds, construct a parametrix and
describe its precise analytic structure. We use this result to study Rockland sequences, a notion generalizing elliptic sequences to filtered manifolds. The main application that we present is to the analysis of the Bernstein–Gelfand–Gelfand (BGG) sequences over regular parabolic geometries. We do this by generalizing the BGG machinery to more general filtered manifolds (in a non-canonical way) and show that the generalized BGG sequences are Rockland in a graded sense.

Originalsprache	Englisch
Seiten (von - bis)	721-789
Seitenumfang	69
Fachzeitschrift	Annals of Global Analysis and Geometry
Jahrgang	62
Ausgabenummer	4
Frühes Online-Datum	2 Sept. 2022
DOIs	https://doi.org/10.1007/s10455-022-09870-0
Publikationsstatus	Veröffentlicht - Nov. 2022

ÖFOS 2012

101002 Analysis
101006 Differentialgeometrie

Zugriff auf Dokument

10.1007/s10455-022-09870-0Lizenz: CC BY 4.0

https://phaidra.univie.ac.at/o:1649452Lizenz: CC BY 4.0

Andere Dateien und Links

1 Laufend
2 Abgeschlossen

Isoperimetrische Struktur von Anfangsdaten der Einstein-Gleichungen
Eichmair, M.
1/01/17 → 31/12/24
Projekt: Forschungsförderung
Analytische Torsion filtrierter Mannigfaltigkeiten
Haller, S.
1/07/19 → 30/06/23
Projekt: Forschungsförderung
Singularitätentheoreme und Comparison Geometry
Kunzinger, M., Steinbauer, R., Vickers, J. A. G. & Grant, J.
1/06/16 → 31/05/21
Projekt: Forschungsförderung

Regularized determinants of the Rumin complex on nilmanifolds with (2,3,5) geometry
Stefan Haller (Invited speaker)
6 Juni 2024
Aktivität: Vorträge › Vortrag › Science to Science

Datei
Analytic torsion of the Rumin complex on filtered 5-manifolds with growth vector (2,3,5)
Stefan Haller (Vortragende*r)
27 Sept. 2022
Aktivität: Vorträge › Vortrag › Science to Science

Datei
Analytic torsion of (2,3,5) geometries
Stefan Haller (Vortragende*r)
22 Juli 2022
Aktivität: Vorträge › Vortrag › Science to Science

Datei

Zitationsweisen

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title = "Graded hypoellipticity of BGG sequences",

abstract = "This article studies hypoellipticity on general filtered manifolds. We extend the Rocklandcriterion to a pseudodifferential calculus on filtered manifolds, construct a parametrix anddescribe its precise analytic structure. We use this result to study Rockland sequences, a notion generalizing elliptic sequences to filtered manifolds. The main application that we present is to the analysis of the Bernstein–Gelfand–Gelfand (BGG) sequences over regular parabolic geometries. We do this by generalizing the BGG machinery to more general filtered manifolds (in a non-canonical way) and show that the generalized BGG sequences are Rockland in a graded sense.",

keywords = "Filtered manifold, Pseudodifferential operator, Hypoelliptic operator, Rockland operator, Hypoelliptic sequence, Rockland sequence, BGG sequence, Rumin–Seshadri operator, Engel structure, Generic rank two distribution in dimension five, SUBELLIPTIC OPERATORS, COMPLEX, Rumin-Seshadri operator, SPACES, ALGEBRA, PSEUDODIFFERENTIAL-OPERATORS, DIFFERENTIAL FORMS, SINGER INDEX FORMULA, HEISENBERG GROUP",

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year = "2022",

month = nov,

doi = "10.1007/s10455-022-09870-0",

language = "English",

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T1 - Graded hypoellipticity of BGG sequences

AU - Dave, Shantanu

AU - Haller, Stefan

PY - 2022/11

Y1 - 2022/11

N2 - This article studies hypoellipticity on general filtered manifolds. We extend the Rocklandcriterion to a pseudodifferential calculus on filtered manifolds, construct a parametrix anddescribe its precise analytic structure. We use this result to study Rockland sequences, a notion generalizing elliptic sequences to filtered manifolds. The main application that we present is to the analysis of the Bernstein–Gelfand–Gelfand (BGG) sequences over regular parabolic geometries. We do this by generalizing the BGG machinery to more general filtered manifolds (in a non-canonical way) and show that the generalized BGG sequences are Rockland in a graded sense.

AB - This article studies hypoellipticity on general filtered manifolds. We extend the Rocklandcriterion to a pseudodifferential calculus on filtered manifolds, construct a parametrix anddescribe its precise analytic structure. We use this result to study Rockland sequences, a notion generalizing elliptic sequences to filtered manifolds. The main application that we present is to the analysis of the Bernstein–Gelfand–Gelfand (BGG) sequences over regular parabolic geometries. We do this by generalizing the BGG machinery to more general filtered manifolds (in a non-canonical way) and show that the generalized BGG sequences are Rockland in a graded sense.

KW - Filtered manifold

KW - Pseudodifferential operator

KW - Hypoelliptic operator

KW - Rockland operator

KW - Hypoelliptic sequence

KW - Rockland sequence

KW - BGG sequence

KW - Rumin–Seshadri operator

KW - Engel structure

KW - Generic rank two distribution in dimension five

KW - SUBELLIPTIC OPERATORS

KW - COMPLEX

KW - Rumin-Seshadri operator

KW - SPACES

KW - ALGEBRA

KW - PSEUDODIFFERENTIAL-OPERATORS

KW - DIFFERENTIAL FORMS

KW - SINGER INDEX FORMULA

KW - HEISENBERG GROUP

UR - https://arxiv.org/abs/2107.02062

UR - http://www.scopus.com/inward/record.url?scp=85137498911&partnerID=8YFLogxK

U2 - 10.1007/s10455-022-09870-0

DO - 10.1007/s10455-022-09870-0

M3 - Article

SN - 0232-704X

VL - 62

SP - 721

EP - 789

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 4

ER -

Graded hypoellipticity of BGG sequences

Abstract

ÖFOS 2012

Zugriff auf Dokument

Andere Dateien und Links

Projekte

Isoperimetrische Struktur von Anfangsdaten der Einstein-Gleichungen

Analytische Torsion filtrierter Mannigfaltigkeiten

Singularitätentheoreme und Comparison Geometry

Aktivitäten

Regularized determinants of the Rumin complex on nilmanifolds with (2,3,5) geometry

Analytic torsion of the Rumin complex on filtered 5-manifolds with growth vector (2,3,5)

Analytic torsion of (2,3,5) geometries

Zitationsweisen