On the Equivariant Reduction of Structure Group of a Principal Bundle to a Levi Subgroup
نویسنده
چکیده
Let M be an irreducible projective variety 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 algebraic group 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 EG, there is a naturally associated conjugacy class of Levi subgroups of G. Given a Levi subgroup H in this conjugacy class, 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 Γ.
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