| Title:
|
Poisson transforms for differential forms (English) |
| Author:
|
Harrach, Christoph |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
52 |
| Issue:
|
5 |
| Year:
|
2016 |
| Pages:
|
303-311 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Poisson transforms |
| Keyword:
|
integral transform of differential forms |
| Keyword:
|
homogeneous spaces |
| MSC:
|
22E46 |
| MSC:
|
53C65 |
| idZBL:
|
Zbl 06674906 |
| idMR:
|
MR3610865 |
| DOI:
|
10.5817/AM2016-5-303 |
| . |
| Date available:
|
2016-12-20T21:56:45Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145937 |
| . |
| Reference:
|
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| Reference:
|
[2] Gaillard, P.-Y.: Transformation de Poisson de formes différentielles. Le cas de l’espace hyperbolique.Comment. Math. Helv 61 (4) (1986), 581–616, (French). Zbl 0636.43007, MR 0870708, 10.1007/BF02621934 |
| Reference:
|
[3] Greub, W., Halperin, S., Vanstone, R.: Connections, curvature, and cohomology.vol. I, Academic Press, 1972. Zbl 0322.58001 |
| Reference:
|
[4] Helgason, S.: Groups and geometric analysis. Integral geometry, invariant differential operators and spherical functions.Pure Appl. Math. (1984). Zbl 0543.58001, MR 1790156 |
| Reference:
|
[5] Helgason, S.: Geometric analysis on symmetric spaces.Mathematical Surveys and Monographs, vol. 39, AMS, 1994. Zbl 0809.53057, MR 1280714 |
| Reference:
|
[6] Thurston, W.: The geometry and topology of three manifolds.Lecture Notes, available online: http://library.msri.org/books/gt3m. |
| Reference:
|
[7] van der Ven, H.: Vector valued Poisson transforms on Riemannian symmetric spaces of rank one.J. Funct. Anal. 119 (1994), 358–400. Zbl 0813.53034, MR 1261097, 10.1006/jfan.1994.1015 |
| Reference:
|
[8] Yang, A.: Vector valued Poisson transforms on Riemannian symmetric spaces.Ph.D. thesis, Massachusetts Institute of Technology, 1994. |
| . |
