| Title:
|
Ellipticity of the symplectic twistor complex (English) |
| Author:
|
Krýsl, Svatopluk |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
309-327 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the symplectic connection is of Ricci type. In this paper, we prove that certain parts of these complexes are elliptic. (English) |
| Keyword:
|
Fedosov manifolds |
| Keyword:
|
Segal-Shale-Weil representation |
| Keyword:
|
Kostant’s spinors |
| Keyword:
|
elliptic complexes |
| MSC:
|
22E46 |
| MSC:
|
53C07 |
| MSC:
|
53C80 |
| MSC:
|
58J05 |
| idZBL:
|
Zbl 1249.22009 |
| idMR:
|
MR2876952 |
| . |
| Date available:
|
2011-12-16T15:19:55Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141778 |
| . |
| Reference:
|
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