Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds

Svatopluk Krýsl

Archivum Mathematicum (2007)

  • Volume: 043, Issue: 5, page 467-484
  • ISSN: 0044-8753

Abstract

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Consider a flat symplectic manifold ( M 2 l , ω ) , l ≥ 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 λ is an eigenvalue of the symplectic Dirac operator such that - ı l λ is not a symplectic Killing number, then l - 1 l λ is an eigenvalue of the symplectic Rarita-Schwinger operator.

How to cite

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Krýsl, Svatopluk. "Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds." Archivum Mathematicum 043.5 (2007): 467-484. <http://eudml.org/doc/250176>.

@article{Krýsl2007,
abstract = {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.},
author = {Krýsl, Svatopluk},
journal = {Archivum Mathematicum},
keywords = {symplectic Dirac operator; symplectic Rarita-Schwinger operator; Kostant symplectic spinors; symplectic Dirac operator; symplectic Rarita-Schwinger operator; Kostant symplectic spinors},
language = {eng},
number = {5},
pages = {467-484},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds},
url = {http://eudml.org/doc/250176},
volume = {043},
year = {2007},
}

TY - JOUR
AU - Krýsl, Svatopluk
TI - Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 5
SP - 467
EP - 484
AB - 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.
LA - eng
KW - symplectic Dirac operator; symplectic Rarita-Schwinger operator; Kostant symplectic spinors; symplectic Dirac operator; symplectic Rarita-Schwinger operator; Kostant symplectic spinors
UR - http://eudml.org/doc/250176
ER -

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