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


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).


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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