| Title:
|
Symplectic Killing spinors (English) |
| Author:
|
Krýsl, Svatopluk |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
19-35 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(M,\omega )$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla$. Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main object of this paper. We derive a necessary condition which has to be satisfied by a symplectic Killing spinor field. Using this condition one may easily compute the symplectic Killing spinor fields for the standard symplectic vector spaces and the round sphere $S^2$ equipped with the volume form of the round metric. (English) |
| Keyword:
|
Fedosov manifolds |
| Keyword:
|
symplectic spinors |
| Keyword:
|
symplectic Killing spinors |
| Keyword:
|
symplectic Dirac operators |
| Keyword:
|
Segal-Shale-Weil representation |
| MSC:
|
53C07 |
| MSC:
|
58J60 |
| idZBL:
|
Zbl 1249.53093 |
| idMR:
|
MR2880908 |
| . |
| Date available:
|
2012-02-07T10:21:24Z |
| Last updated:
|
2014-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141823 |
| . |
| Reference:
|
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