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

Algebraic Geometry 2021-05-25 v1 Mathematical Physics math.MP Symplectic Geometry

Abstract

We address quantization of the natural symplectic structure on a moduli space of parabolic vector bundles of parabolic degree zero over CP1\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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Cite

@article{arxiv.1111.4838,
  title  = {Quantization of some moduli spaces of parabolic vector bundles on CP^1},
  author = {Indranil Biswas and Carlos Florentino and José Mourão and João P. Nunes},
  journal= {arXiv preprint arXiv:1111.4838},
  year   = {2021}
}

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17 pages