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18 January 2022
  » arxiv » math.AG/0310035

 Article overview

On the equivariant reduction of structure group of a principal bundle to a Levi subgroup
Indranil Biswas an A. J. Parameswaran ;
Date 3 Oct 2003
Subject Algebraic Geometry; Algebraic Topology MSC-class: 14L40; 14L30 | math.AG math.AT
AbstractLet $M$ be an irreducible projective variety over an algebraically closed field $k$ of characteristic zero equipped with an action of a group $Gamma$. Let $E_G$ be a principal $G$--bundle over $M$, where $G$ is a connected reductive algebraic group over $k$, equipped with a lift of the action of $Gamma$ on $M$. We give conditions for $E_G$ to admit a $Gamma$--equivariant reduction of structure group to $H$, where $H subset G$ is a Levi subgroup. We show that for $E_G$, there is a naturally associated conjugacy class of Levi subgroups of $G$. Given a Levi subgroup $H$ in this conjugacy class, $E_G$ admits a $Gamma$--equivariant reduction of structure group to $H$, and furthermore, such a reduction is unique up to an automorphism of $E_G$ that commutes with the action of $Gamma$.
Source arXiv, math.AG/0310035
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