Singular BGG sequences for the even orthogonal case

Lukáš Krump; Vladimír Souček

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 267-278
  • ISSN: 0044-8753

Abstract

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Locally exact complexes of invariant differential operators are constructed on the homogeneous model for a parabolic geometry for the even orthogonal group. The tool used for the construction is the Penrose transform developed by R. Baston and M. Eastwood. Complexes constructed here belong to the singular infinitesimal character.

How to cite

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Krump, Lukáš, and Souček, Vladimír. "Singular BGG sequences for the even orthogonal case." Archivum Mathematicum 042.5 (2006): 267-278. <http://eudml.org/doc/249829>.

@article{Krump2006,
abstract = {Locally exact complexes of invariant differential operators are constructed on the homogeneous model for a parabolic geometry for the even orthogonal group. The tool used for the construction is the Penrose transform developed by R. Baston and M. Eastwood. Complexes constructed here belong to the singular infinitesimal character.},
author = {Krump, Lukáš, Souček, Vladimír},
journal = {Archivum Mathematicum},
keywords = {BGG sequence; invariant differential operator; parabolic geometry; Penrose transform},
language = {eng},
number = {5},
pages = {267-278},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Singular BGG sequences for the even orthogonal case},
url = {http://eudml.org/doc/249829},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Krump, Lukáš
AU - Souček, Vladimír
TI - Singular BGG sequences for the even orthogonal case
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 267
EP - 278
AB - Locally exact complexes of invariant differential operators are constructed on the homogeneous model for a parabolic geometry for the even orthogonal group. The tool used for the construction is the Penrose transform developed by R. Baston and M. Eastwood. Complexes constructed here belong to the singular infinitesimal character.
LA - eng
KW - BGG sequence; invariant differential operator; parabolic geometry; Penrose transform
UR - http://eudml.org/doc/249829
ER -

References

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  1. Baston R., Quaternionic complexes, J. Geom. Phys. 8 (1992), 29–52. (1992) Zbl0764.53022MR1165872
  2. Baston R. J., Eastwood M. G., Penrose transform; Its interaction with representation theory, Clarendon Press, Oxford, 1989. (1989) Zbl0726.58004MR1038279
  3. Calderbank D. M. J., Diemer T., Differential invariants and curved Bernstein–Gelfand–Gelfand sequences, J. Reine angew. Math. 537 (2001), 67–103. Zbl0985.58002MR1856258
  4. Čap A., Two constructions with parabolic geometries, preprint, arXiv:math.DG/0504389 Zbl1120.53013MR2287124
  5. Čap A., Schichl H., Parabolic geometries and canonical Cartan connections, Hokkaido Math. J. 29 3 (2000), 453–505. Zbl0996.53023MR1795487
  6. Čap A., Slovák J., Souček V., Bernstein-Gelfand-Gelfand sequences, Ann. of Math. (2) 154 1 (2001), 97–113. MR1847589
  7. Colombo F., Sabadini A., Sommen F., Struppa D., Analysis of Dirac systems and computational algebra, Birkhäuser, Basel, 2004. Zbl1064.30049MR2089988
  8. Franek P., Generalized Verma module homomorphisms in singular character, submitted to Proc. of the Winter School ’Geometry and Physics’, Srni, 2006. Zbl1164.22310MR2322409
  9. Krump L., Construction of BGG sequences for AHS structures, Comment. Math. Univ. Carolin. 42 1 (2001), 31–52, Zbl1054.53071MR1825371
  10. Krump L., Souček V., Hasse diagrams for parabolic geometries, Proc. of ’The 22nd Winter School ’Geometry and Physics’, Srní 2002, Rend. Circ. Mat. Palermo (2) Suppl. 71 (2003). Zbl1047.53014MR1982440
  11. Nacinovich M., Complex analysis and complexes of differential operators, LNM 950, Springer-Verlag, Berlin, 1980. (1980) MR0672785
  12. Sharpe R. W., Differential geometry, Grad. Texts in Math. 166 (1997). (1997) Zbl0876.53001MR1453120
  13. Slovák J., Parabolic geometries, Research Lecture Notes, Part of DrSc. Dissertation, Preprint IGA 11/97, electronically available at www.maths.adelaide.edu.au. 
  14. Šmíd D., The BGG diagram for contact orthogonal geometry of even dimension, Acta Univ. Carolin. Math. Phys. 45 (2004), 79–96. Zbl1138.17310MR2109696

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