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.

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

References in corpus (10)

• On the tangent groupoid of a filtered manifold
• Parabolic induction and restriction via C*-algebras and Hilbert C*-modules
• Graded hypoellipticity of BGG sequences
• On Nurowski's conformal structure associated to a generic rank two distribution in dimension five
• Tangent Maps and Tangent Groupoid for Carnot Manifolds
• The heat asymptotics on filtered manifolds
• Relative BGG sequences; II. BGG machinery and invariant operators
• On the deformation groupoid of the inhomogeneous pseudo-differential Calculus
• On 5-manifolds admitting rank two distributions of Cartan type
• Analytic torsion of generic rank two distributions in dimension five

Cited by in corpus (11)

• Graded hypoellipticity of BGG sequences
• Analytic torsion of generic rank two distributions in dimension five
• Index theorem for inhomogeneous hypoelliptic differential operators
• Pseudodifferential operators on filtered manifolds as generalized fixed points
• Sub-Riemannian limit of the differential form heat kernels of contact manifolds
• Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates
• Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group
• Analytic torsion of nilmanifolds with (2,3,5) distributions
• A transverse index theorem in the calculus of filtered manifolds
• A groupoid approach to the Wodzicki residue
• Shubin calculi for actions of graded Lie groups