The Poisson transform for higher order differential operators. (English) Zbl 1105.43005

Slovák, Jan (ed.) et al., The proceedings of the 24th winter school “Geometry and physics”, Srní, Czech Republic, January 17–24, 2004. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 75, 317-323 (2005).
From the abstract: The Poisson transform maps sections of vector bundles over a parabolic geometry \(G/P\) to sections of vector bundles over a symmetric space \(G/K\). The parabolic geometry can be understood as a (part of the) boundary of the symmetric space. We show that the Poisson transform intertwines invariant differential operators on these spaces, generalizing the results of Ørsted and Koranyi and Reimann.
For the entire collection see [Zbl 1074.53001].


43A85 Harmonic analysis on homogeneous spaces
53C10 \(G\)-structures
53C35 Differential geometry of symmetric spaces