On spherical nilpotent orbits and beyond

Dmitri I. Panyushev

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 5, page 1453-1476
  • ISSN: 0373-0956

Abstract

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We continue investigations that are concerned with the complexity of nilpotent orbits in semisimple Lie algebras. We give a characterization of the spherical nilpotent orbits in terms of minimal Levi subalgebras intersecting them. This provides a kind of canonical form for such orbits. A description minimal non-spherical orbits in all simple Lie algebras is obtained. The theory developed for the adjoint representation is then extended to Vinberg’s θ -groups. This yields a description of spherical nilpotent orbits for the isotropy representation of a symmetric variety.

How to cite

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Panyushev, Dmitri I.. "On spherical nilpotent orbits and beyond." Annales de l'institut Fourier 49.5 (1999): 1453-1476. <http://eudml.org/doc/75390>.

@article{Panyushev1999,
abstract = {We continue investigations that are concerned with the complexity of nilpotent orbits in semisimple Lie algebras. We give a characterization of the spherical nilpotent orbits in terms of minimal Levi subalgebras intersecting them. This provides a kind of canonical form for such orbits. A description minimal non-spherical orbits in all simple Lie algebras is obtained. The theory developed for the adjoint representation is then extended to Vinberg’s $\theta $-groups. This yields a description of spherical nilpotent orbits for the isotropy representation of a symmetric variety.},
author = {Panyushev, Dmitri I.},
journal = {Annales de l'institut Fourier},
keywords = {semisimple Lie algebra; nilpotent orbit; spherical variety},
language = {eng},
number = {5},
pages = {1453-1476},
publisher = {Association des Annales de l'Institut Fourier},
title = {On spherical nilpotent orbits and beyond},
url = {http://eudml.org/doc/75390},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Panyushev, Dmitri I.
TI - On spherical nilpotent orbits and beyond
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 5
SP - 1453
EP - 1476
AB - We continue investigations that are concerned with the complexity of nilpotent orbits in semisimple Lie algebras. We give a characterization of the spherical nilpotent orbits in terms of minimal Levi subalgebras intersecting them. This provides a kind of canonical form for such orbits. A description minimal non-spherical orbits in all simple Lie algebras is obtained. The theory developed for the adjoint representation is then extended to Vinberg’s $\theta $-groups. This yields a description of spherical nilpotent orbits for the isotropy representation of a symmetric variety.
LA - eng
KW - semisimple Lie algebra; nilpotent orbit; spherical variety
UR - http://eudml.org/doc/75390
ER -

References

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