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Annals of Global Analysis and Geometry

, Volume 43, Issue 2, pp 161–176 | Cite as

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

  • Indranil Biswas
  • Carlos FlorentinoEmail author
  • José Mourão
  • João P. Nunes
Original Paper
  • 126 Downloads

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).

Keywords

Quantization Parabolic bundles Moduli space Elliptic curve 

Mathematics Subject Classification (2000)

53D50 14H60 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Indranil Biswas
    • 1
  • Carlos Florentino
    • 2
    Email author
  • José Mourão
    • 2
  • João P. Nunes
    • 2
  1. 1.School of MathematicsTata Institute of Fundamental ResearchBombayIndia
  2. 2.Department of Mathematics, Center for Mathematical Analysis, Geometry and Dynamical SystemsInstituto Superior TécnicoLisbonPortugal

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