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Communications in Mathematical Physics

, Volume 164, Issue 2, pp 385–419 | Cite as

Conformal blocks and generalized theta functions

  • Arnaud Beauville
  • Yves Laszlo
Article

Abstract

LetSU X r be the moduli space of rankr vector bundles with trivial determinant on a Riemann surfaceX. This space carries a natural line bundle, the determinant line bundleL. We describe a canonical isomorphism of the space of global sections ofL k with the space of conformal blocks defined in terms of representations of the Lie algebrasl r (C((z))). It follows in particular that the dimension ofH0(SU X r,L k ) is given by the Verlinde formula.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Modulus Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Arnaud Beauville
    • 1
  • Yves Laszlo
    • 1
  1. 1.URA 752 du CNRS, Mathématiques-Bât 425Université Paris-SudOrsay CedexFrance

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