| Title:
|
Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds (English) |
| Author:
|
Krýsl, Svatopluk |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
5 |
| Year:
|
2007 |
| Pages:
|
467-484 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Consider a flat symplectic manifold $(M^{2l},\omega )$, $l\ge 2$, admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If $\lambda $ is an eigenvalue of the symplectic Dirac operator such that $-\imath l \lambda $ is not a symplectic Killing number, then $\frac{l-1}{l}\lambda $ is an eigenvalue of the symplectic Rarita-Schwinger operator. (English) |
| Keyword:
|
symplectic Dirac operator |
| Keyword:
|
symplectic Rarita-Schwinger operator |
| Keyword:
|
Kostant symplectic spinors |
| MSC:
|
35N10 |
| MSC:
|
53D05 |
| MSC:
|
58J05 |
| MSC:
|
58J50 |
| MSC:
|
58Jxx |
| idZBL:
|
Zbl 1199.58011 |
| idMR:
|
MR2381789 |
| . |
| Date available:
|
2008-06-06T22:52:14Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108085 |
| . |
| Reference:
|
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