Spherical roots of spherical varieties

Friedrich Knop[1]

  • [1] Department Mathematik, Emmy-Noether-Zentrum, FAU Erlangen-Nürnberg, Cauerstraße 11, 91058 Erlangen, Germany

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 6, page 2503-2526
  • ISSN: 0373-0956

Abstract

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Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer’s classification of spherical varieties of rank 1.

How to cite

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Knop, Friedrich. "Spherical roots of spherical varieties." Annales de l’institut Fourier 64.6 (2014): 2503-2526. <http://eudml.org/doc/275467>.

@article{Knop2014,
abstract = {Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer’s classification of spherical varieties of rank 1.},
affiliation = {Department Mathematik, Emmy-Noether-Zentrum, FAU Erlangen-Nürnberg, Cauerstraße 11, 91058 Erlangen, Germany},
author = {Knop, Friedrich},
journal = {Annales de l’institut Fourier},
keywords = {Spherical varieties; spherical roots; homogeneous varieties; fields of positive characteristic; spherical varieties},
language = {eng},
number = {6},
pages = {2503-2526},
publisher = {Association des Annales de l’institut Fourier},
title = {Spherical roots of spherical varieties},
url = {http://eudml.org/doc/275467},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Knop, Friedrich
TI - Spherical roots of spherical varieties
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 6
SP - 2503
EP - 2526
AB - Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer’s classification of spherical varieties of rank 1.
LA - eng
KW - Spherical varieties; spherical roots; homogeneous varieties; fields of positive characteristic; spherical varieties
UR - http://eudml.org/doc/275467
ER -

References

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