# Poisson transforms for differential forms

## Christoph Harrach

Address: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

E-mail: christoph.harrach@univie.ac.at

Abstract: We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite dimensional representations of reductive Lie groups. Moreover, we will explicitly generate a family of degree-preserving Poisson transforms whose restriction to real valued differential forms has coclosed images. In addition, as a transform on sections of density bundles it can be related to the classical Poisson transform, proving that we produced a natural generalization of the classical theory.

AMSclassification: primary 53C65; secondary 22E46.

Keywords: Poisson transforms, integral transform of differential forms, homogeneous spaces.

DOI: 10.5817/AM2016-5-303