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math.DG2024
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…
math.DG2024
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…
math.DG2024
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 specific Poisson transforms mapping differential forms on the sphere endowed with its natural CR structure to forms on complex hy…