| Popis: |
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 E G 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 E G 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 E G , 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 E G admits a Γ-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 Γ on E G . |
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