6 papers · 1 filter
A new construction of the Riemannian deformation sequence
Andreas Cap
We obtain a new construction of a sequence of invariant differential operators on a Riemannian manifold that governs the linearized deformation theory of . Starting from…
The Bernstein-Gelfand-Gelfand (BGG) Construction: Algebra, Geometry, and Analysis; Part I
Andreas Cap
These are lecture notes for the first part of a short course that I taught jointly with Kaibo Hu as part of the thematic program "Differential Complexes: Theory, Discretization, an…
BGG Sequences -- A Riemannian perspective
Andreas Cap
BGG resolutions and generalized BGG resolutions from representation theory of semisimple Lie algebras have been generalized to sequences of invariant differential operators on mani…
Partial AHS-Structures, their Cartan description and partial BGG sequences
Andreas Cap, Micha Andrzej Wasilewicz
G-structures and Cartan geometries are two major approaches to the description of geometric structures (in the sense of differential geometry) on manifolds of some fixed dimension…
On Relative Tractor Bundles
Andreas Čap, Zhangwen Guo, Michał Andrzej Wasilewicz
This article contributes to the relative BGG-machinery for parabolic geometries. Starting from a relative tractor bundle, this machinery constructs a sequence of differential opera…
Poisson transforms, the BGG complex, and discrete series representations of SU(n+1,1)
Andreas Cap, Christoph Harrach, Pierre Julg
The aim of this article is to construct a specific Poisson transform mapping differential forms on the sphere endowed with its natural CR structure to forms on complex h…