On the equivariant reduction of structure group of a principal bundle to a Levi subgroup

Details On the equivariant reduction of structure group of a principal bundle to a Levi subgroup On the equivariant reduction of structure group of a principal bundle to a Levi subgroup

2003-10-03

arxiv.org/abs/math/0310035v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

Let $M$ 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 $\Gamma$.

Affiliated with

Also associated with

No associations

Rating

On the equivariant reduction of structure group of a principal bundle to a Levi subgroup does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the equivariant reduction of structure group of a principal bundle to a Levi subgroup, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the equivariant reduction of structure group of a principal bundle to a Levi subgroup will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-571350