Symplectic spinor valued forms and invariant operators acting between them

Svatopluk Krýsl

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 279-290
  • ISSN: 0044-8753

Abstract

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Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.

How to cite

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Krýsl, Svatopluk. "Symplectic spinor valued forms and invariant operators acting between them." Archivum Mathematicum 042.5 (2006): 279-290. <http://eudml.org/doc/249824>.

@article{Krýsl2006,
abstract = {Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.},
author = {Krýsl, Svatopluk},
journal = {Archivum Mathematicum},
keywords = {symplectic geometry; symplectic spinors; metaplectic structure; higher symplectic spinor module; torsion-free connection},
language = {eng},
number = {5},
pages = {279-290},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Symplectic spinor valued forms and invariant operators acting between them},
url = {http://eudml.org/doc/249824},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Krýsl, Svatopluk
TI - Symplectic spinor valued forms and invariant operators acting between them
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 279
EP - 290
AB - Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.
LA - eng
KW - symplectic geometry; symplectic spinors; metaplectic structure; higher symplectic spinor module; torsion-free connection
UR - http://eudml.org/doc/249824
ER -

References

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  12. Klein A., Eine Fouriertransformation für symplektische Spinoren und Anwendungen in der Quantisierung, Diploma Thesis, Technische Universität Berlin, Berlin, 2000. 
  13. Kostant B., On the Tensor Product of a Finite and an Infinite Dimensional Representations, J. Funct. Anal. 20 (1975), 257–285. (1975) MR0414796
  14. Kostant B., Symplectic Spinors, Sympos. Math. XIV (1974), 139–152. (1974) Zbl0321.58015MR0400304
  15. Krýsl S., Invariant differential operators for contact projective geometries, Ph.D. thesis, Charles University Prague, Prague, 2004. 
  16. Krýsl S., Decomposition of the tensor product of the defining representation and a higher symplectic spinor module over 𝔰𝔭 ( 2 n , ℂ ) , to appear in J. Lie Theory 17, No. 1 (2007), 63–72. MR2286881
  17. Reuter M., Symplectic Dirac-Kähler Fields, J. Math. Phys. 40 (1999), 5593–5640; electronically available at hep-th/9910085. (1999) Zbl0968.81037MR1722329

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