Quantization of some moduli spaces of parabolic vector bundles on $${{\mathbb C}{\mathbb P}^1}$$

Abstract

We address quantization of the natural symplectic structure on a moduli space of parabolic vector bundles of parabolic degree zero over CP 1 with four parabolic points and parabolic weights in {0, 1/2}. Identifying such parabolic bundles as vector bundles on an elliptic curve, we obtain explicit expressions for the corresponding non-abelian theta functions. These non-abelian theta functions are described in terms of certain naturally defined distributions on the compact group SU(2).