Ellipticity of the symplectic twistor complex

Svatopluk Krýsl

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 4, page 309-327
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Krýsl, Svatopluk. "Ellipticity of the symplectic twistor complex." Archivum Mathematicum 047.4 (2011): 309-327. <http://eudml.org/doc/246918>.

@article{Krýsl2011,
abstract = {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.},
author = {Krýsl, Svatopluk},
journal = {Archivum Mathematicum},
keywords = {Fedosov manifolds; Segal-Shale-Weil representation; Kostant’s spinors; elliptic complexes; Fedosov manifold; Segal-Shale-Weil representation; Kostant's spinor; elliptic complexes},
language = {eng},
number = {4},
pages = {309-327},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Ellipticity of the symplectic twistor complex},
url = {http://eudml.org/doc/246918},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Krýsl, Svatopluk
TI - Ellipticity of the symplectic twistor complex
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 4
SP - 309
EP - 327
AB - 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.
LA - eng
KW - Fedosov manifolds; Segal-Shale-Weil representation; Kostant’s spinors; elliptic complexes; Fedosov manifold; Segal-Shale-Weil representation; Kostant's spinor; elliptic complexes
UR - http://eudml.org/doc/246918
ER -

References

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