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 ofH 0(SU X r,L k) is given by the Verlinde formula.
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Communicated by G. Felder
Both authors were partially supported by the European Science Project “Geometry of Algebraic Varieties,” Contract no. SCI-0398-C(A)
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Beauville, A., Laszlo, Y. Conformal blocks and generalized theta functions. Commun.Math. Phys. 164, 385–419 (1994). https://doi.org/10.1007/BF02101707
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DOI: https://doi.org/10.1007/BF02101707