Christoph Harrach (University of Vienna): Poisson transforms adapted to BGG-complexes
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2021-09-27

Christoph Harrach (University of Vienna).
Poisson transforms adapted to BGG-complexes.
We consider intertwining operators for tractor bundle valued differential forms between homogeneous parabolic geometries G/P and their corresponding Riemannian symmetric spaces G/K which are compatible with the BGG-complex and relate this property to differential operators on G/K. Furthermore, we give an explicit construction of such operators in terms of Poisson transforms, which are integral operators with an invariant kernel. Explicitly, we translate existence and compatibility of Poisson transforms with several differential operators to computations in finite dimensional representations of reductive Lie groups.

GRIEG collaboration project: SCREAM workshop 2021.