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

Biswas, Indranil ; Parameswaran, A. J. (2006) On the equivariant reduction of structure group of a principal bundle to a Levi subgroup Journal de Mathematiques Pures et Appliques, 85 (1). pp. 54-70. ISSN 0021-7824

Full text not available from this repository.

Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00217...

Related URL: http://dx.doi.org/10.1016/j.matpur.2005.10.007

Abstract

Let M be an irreducible projective variety, defined over an algebraically closed field k of characteristic zero, equipped with an action of a group Γ. Let EG be a principal G-bundle over M, where G is a connected reductive linear algebraic group defined over k, equipped with a lift of the action of Γ on M. We give conditions for EG to admit a Γ-equivariant reduction of structure group to H, where H⊂G is a Levi subgroup. We show that for any principal G-bundle EG, there is a naturally associated conjugacy class of Levi subgroups of G. Given a Levi subgroup H in this conjugacy class, the principal G-bundle EG admits a Γ-equivariant reduction of structure group to H, and furthermore, such a reduction is unique up to an automorphism of EG that commutes with the action of ? on EG.

Item Type:Article
Keywords:Principal Bundle; Levi Subgroup; Automorphism Group; Reduction
ID Code:35276
Deposited On:04 Jul 2012 13:27
Last Modified:04 Jul 2012 13:27

Repository Staff Only: item control page