On deformation method in invariant theory

Dmitri Panyushev

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 4, page 985-1012
  • ISSN: 0373-0956

Abstract

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In this paper we relate the deformation method in invariant theory to spherical subgroups. Let G be a reductive group, Z an affine G -variety and H ⊂ G a spherical subgroup. We show that whenever G / H is affine and its semigroup of weights is saturated, the algebra of H -invariant regular functions on Z has a G -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of G . The deformation method in its usual form, as developed by Luna et al., is a particular case of this construction. Our result also applies to the description of invariants of some reducible representations of reductive groups.New applications of the deformation method are given which concern the property of being complete intersection for algebras of invariants. We also give some applications of the deformation method to doubled actions.

How to cite

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Panyushev, Dmitri. "On deformation method in invariant theory." Annales de l'institut Fourier 47.4 (1997): 985-1012. <http://eudml.org/doc/75262>.

@article{Panyushev1997,
abstract = {In this paper we relate the deformation method in invariant theory to spherical subgroups. Let $G$ be a reductive group, $Z$ an affine $G$-variety and $H\subset G$ a spherical subgroup. We show that whenever $G/H$ is affine and its semigroup of weights is saturated, the algebra of $H$-invariant regular functions on $Z$ has a $G$-invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of $G$. The deformation method in its usual form, as developed by Luna et al., is a particular case of this construction. Our result also applies to the description of invariants of some reducible representations of reductive groups.New applications of the deformation method are given which concern the property of being complete intersection for algebras of invariants. We also give some applications of the deformation method to doubled actions.},
author = {Panyushev, Dmitri},
journal = {Annales de l'institut Fourier},
keywords = {algebra of invariants; reductive group action; complete intersection; spherical variety; deformation},
language = {eng},
number = {4},
pages = {985-1012},
publisher = {Association des Annales de l'Institut Fourier},
title = {On deformation method in invariant theory},
url = {http://eudml.org/doc/75262},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Panyushev, Dmitri
TI - On deformation method in invariant theory
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 4
SP - 985
EP - 1012
AB - In this paper we relate the deformation method in invariant theory to spherical subgroups. Let $G$ be a reductive group, $Z$ an affine $G$-variety and $H\subset G$ a spherical subgroup. We show that whenever $G/H$ is affine and its semigroup of weights is saturated, the algebra of $H$-invariant regular functions on $Z$ has a $G$-invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of $G$. The deformation method in its usual form, as developed by Luna et al., is a particular case of this construction. Our result also applies to the description of invariants of some reducible representations of reductive groups.New applications of the deformation method are given which concern the property of being complete intersection for algebras of invariants. We also give some applications of the deformation method to doubled actions.
LA - eng
KW - algebra of invariants; reductive group action; complete intersection; spherical variety; deformation
UR - http://eudml.org/doc/75262
ER -

References

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