Poisson transforms adapted to BGG-complexes

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Abstract

We present a new construction of Poisson transforms between vector bundle valued differential forms on homogeneous parabolic geometries and vector bundle valued differential forms on the corresponding Riemannian symmetric space, which can be described in terms of finite dimensional representations of reductive Lie groups. In particular, we use these operators to relate the BGG-sequences on the domain to twisted deRham sequences on the target space. Finally, we explicitly design a family of Poisson transforms between standard tractor valued differential forms for the real hyperbolic space and its boundary which are compatible with the BGG-complex.

MSC

53C65
53A30
43A85
35J05

Keywords

Poisson transforms
BGG-operators
Integral geometry
Conformal geometry
Riemannian symmetric spaces

Cited by (0)

This work was supported by project P27072-N25 of the Austrian Science Fund (FWF).