The loop space LP1 of the Riemann sphere consisting of all C or Sobolev W k,p maps S → P1 is an infinite dimensional complex manifold. The loop group LPGL(2, C) acts on LP1. We prove that the group of LPGL(2, C) invariant holomorphic line bundles on LP1 is isomorphic to an infinite dimensional Lie group. Further, we prove that the space of holomorphic… (More)
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