EQUIVARIANT PRINCIPAL BUNDLES OVER THE COMPLEX PROJECTIVE LINE

摘要

Let G be a connected complex reductive linear algebraic group, and let K C G be a maximal compact subgroup of it. Let Eg be a holomorphic principal G-bundles over the complex projective line CP~1 and E_k ∩ Eg a C~∞ reduction of structure group of Eg to K. We consider all pairs (E_g,E_k) of this type such that the total space of E_k is equipped with a C∞ lift of the standard action of SU(2) on CP1 which satisfies the following two conditions: the actions of K and SU(2) on Ek commute, and for each element g ∈ SU(2), the induced action of g on E_g is holomorphic. We give a classification of the isomorphism classes of all such objects.