Holomorphic Hermitian vector bundles over the Riemann sphere

We give a complete classification of isomorphism classes of all SU(2)-equivariant holomorphic Hermitian vector bundles on CP1. We construct a canonical bijective correspondence between the isomorphism classes of SU(2)-equivariant holomorphic Hermitian vector bundles on CP1 and the isomorphism classes of pairs ({Hn}n∈Z,T), where each Hn is a finite dimensional Hilbert space with Hn=0 for all but finitely many n, and T is a linear operator on the direct sum ⊕n∈ZHn such that T(Hn)⊂Hn+2 for all n.