Title
Graded hypoellipticity of BGG sequences
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.
Keywords
Filtered manifoldPseudodifferential operatorHypoelliptic operatorRockland operatorHypoelliptic sequenceRockland sequenceBGG sequenceRumin–Seshadri operatorEngel structureGeneric rank two distribution in dimension five
Object type
Language
English [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:1649452
Appeared in
Title
Annals of Global Analysis and Geometry
Volume
62
Issue
4
ISSN
0232-704X
Issued
2022
From page
721
To page
789
Publisher
Springer Science and Business Media LLC
Date issued
2022
Access rights
Rights statement
© The Author(s) 2022

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