Projective structure, SL ˜ ( 3 , ℝ ) and the symplectic Dirac operator

Marie Holíková; Libor Křižka; Petr Somberg

Archivum Mathematicum (2016)

  • Volume: 052, Issue: 5, page 313-324
  • ISSN: 0044-8753

Abstract

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Inspired by the results on symmetries of the symplectic Dirac operator, we realize symplectic spinor fields and the symplectic Dirac operator in the framework of (the double cover of) homogeneous projective structure in two real dimensions. The symmetry group of the homogeneous model of the double cover of projective geometry in two real dimensions is ˜ ( 3 , ) .

How to cite

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Holíková, Marie, Křižka, Libor, and Somberg, Petr. "Projective structure, $\widetilde{\operatorname{SL}}(3,\mathbb {R})$ and the symplectic Dirac operator." Archivum Mathematicum 052.5 (2016): 313-324. <http://eudml.org/doc/287573>.

@article{Holíková2016,
abstract = {Inspired by the results on symmetries of the symplectic Dirac operator, we realize symplectic spinor fields and the symplectic Dirac operator in the framework of (the double cover of) homogeneous projective structure in two real dimensions. The symmetry group of the homogeneous model of the double cover of projective geometry in two real dimensions is $\{\widetilde\{\}\}(3,)$.},
author = {Holíková, Marie, Křižka, Libor, Somberg, Petr},
journal = {Archivum Mathematicum},
keywords = {projective structure; Segal-Shale-Weil representation; generalized Verma modules; symplectic Dirac operator; $(3,)$},
language = {eng},
number = {5},
pages = {313-324},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Projective structure, $\widetilde\{\operatorname\{SL\}\}(3,\mathbb \{R\})$ and the symplectic Dirac operator},
url = {http://eudml.org/doc/287573},
volume = {052},
year = {2016},
}

TY - JOUR
AU - Holíková, Marie
AU - Křižka, Libor
AU - Somberg, Petr
TI - Projective structure, $\widetilde{\operatorname{SL}}(3,\mathbb {R})$ and the symplectic Dirac operator
JO - Archivum Mathematicum
PY - 2016
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 052
IS - 5
SP - 313
EP - 324
AB - Inspired by the results on symmetries of the symplectic Dirac operator, we realize symplectic spinor fields and the symplectic Dirac operator in the framework of (the double cover of) homogeneous projective structure in two real dimensions. The symmetry group of the homogeneous model of the double cover of projective geometry in two real dimensions is ${\widetilde{}}(3,)$.
LA - eng
KW - projective structure; Segal-Shale-Weil representation; generalized Verma modules; symplectic Dirac operator; $(3,)$
UR - http://eudml.org/doc/287573
ER -

References

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  8. Křižka, L., Somberg, P., Algebraic analysis of scalar generalized Verma modules of Heisenberg parabolic type I.: A n -series, arXiv:1502.07095, to appear in Transformation Groups, 2015. MR3449111
  9. Křižka, L., Somberg, P., Algebraic analysis on scalar generalized Verma modules of Heisenberg parabolic type II.: C n , D n -series, (in preparation). 
  10. Ørsted, B., Generalized gradients and Poisson transforms, Global analysis and harmonic analysis, Sémin. Congr., vol. 4, Soc. Math. France, Paris, 2000, pp. 235–249. (2000) Zbl0989.22018MR1822363
  11. Somberg, P., Šilhan, J., Higher symmetries of the symplectic Dirac operator, (in preparation). 
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  13. Wolf, J.A., Unitary representations of maximal parabolic subgroups of the classical groups, Mem. Amer. Math. Soc., vol. 8, American Mathematical Society, Providence, 1976. (1976) Zbl0344.22016MR0444847

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