Graded hypoellipticity of BGG sequences

Dave, Shantanu; Haller, Stefan

doi:10.1007/s10455-022-09870-0

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Graded hypoellipticity of BGG sequences

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Haller, Stefan
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s10455-022-09870-0
(Publisher version)

https://doi.org/10.48550/arXiv.1705.01659
(Preprint)

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Citation

Dave, S., & Haller, S. (2022). Graded hypoellipticity of BGG sequences. Annals of Global Analysis and Geometry, 62(4), 721-789. doi:10.1007/s10455-022-09870-0.

Cite as: https://hdl.handle.net/21.11116/0000-000B-3633-F

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.