Generalized Verma module homomorphisms in singular character

Peter Franek

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 229-240
  • ISSN: 0044-8753

Abstract

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In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the k -th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac operator in several variables.

How to cite

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Franek, Peter. "Generalized Verma module homomorphisms in singular character." Archivum Mathematicum 042.5 (2006): 229-240. <http://eudml.org/doc/249813>.

@article{Franek2006,
abstract = {In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the $k$-th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac operator in several variables.},
author = {Franek, Peter},
journal = {Archivum Mathematicum},
keywords = {parabolic structure; invariant differential operator; Dirac operator; Verma module},
language = {eng},
number = {5},
pages = {229-240},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Generalized Verma module homomorphisms in singular character},
url = {http://eudml.org/doc/249813},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Franek, Peter
TI - Generalized Verma module homomorphisms in singular character
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 229
EP - 240
AB - In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the $k$-th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac operator in several variables.
LA - eng
KW - parabolic structure; invariant differential operator; Dirac operator; Verma module
UR - http://eudml.org/doc/249813
ER -

References

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  1. Cap A., Slovák J., Parabolic geometries, preprint Zbl1183.53002
  2. Eastwood M., Conformally invariant differential operators on Minkowski space and their curved analogues, Comm. Math. Phys. bf 109 2 (1987), 207–228. (1987) Zbl0659.53047MR0880414
  3. Goodman R., Wallach N., Representations and invariants of the classical groups, Cambgidge University Press, Cambridge, 1998. (1998) Zbl0901.22001MR1606831
  4. Slovák J., Souček V., Invariant operators of the first order on manifolds with a given parabolic structure, Seminarires et congres 4, SMF, 2000, 251-276. Zbl0998.53021MR1822364
  5. Bureš J., Souček V., Regular spinor valued mappings, Seminarii di Geometria, Bologna 1984, ed. S. Coen, Bologna, 1986, 7–22. (1984) MR0877529

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