Geodesic
Poisson transforms for differential forms
Archivum mathematicum, Tome 52 (2016) no. 5, pp. 303-311 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2016-5-303
Classification : 22E46, 53C65
Keywords: Poisson transforms; integral transform of differential forms; homogeneous spaces 
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Harrach, Christoph. Poisson transforms for differential forms. Archivum mathematicum, Tome 52 (2016) no. 5, pp. 303-311. doi: 10.5817/AM2016-5-303

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