Quantization of some moduli spaces of parabolic vector bundles on CP^1

Details Quantization of some moduli spaces of parabolic vector bundles on CP^1 Quantization of some moduli spaces of parabolic vector bundles on CP^1

2011-11-21

arxiv.org/abs/1111.4838v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

We address quantization of the natural symplectic structure on a moduli space of parabolic vector bundles of parabolic degree zero over $\mathbf{CP}^1$ 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).

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