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
Cite
@article{arxiv.1705.01659,
title = {Graded hypoellipticity of BGG sequences},
author = {Shantanu Dave and Stefan Haller},
journal= {arXiv preprint arXiv:1705.01659},
year = {2023}
}
Comments
This version of the article has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10455-022-09870-0