Abstract
We address quantization of the natural symplectic structure on a moduli space of parabolic vector bundles of parabolic degree zero over \({{\mathbb C}{\mathbb P}^1}\) 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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Biswas, I., Florentino, C., Mourão, J. et al. Quantization of some moduli spaces of parabolic vector bundles on \({{\mathbb C}{\mathbb P}^1}\) . Ann Glob Anal Geom 43, 161–176 (2013). https://doi.org/10.1007/s10455-012-9340-2
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DOI: https://doi.org/10.1007/s10455-012-9340-2