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arXiv · alg-geom/9309003

Conformal blocks and generalized theta functions

Arnaud Beauville·Yves Laszlo
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Abstract

Let M(r) be the moduli space of rank r vector bundles with trivial determinant on a Riemann surface X . This space carries a natural line bundle, the determinant line bundle L . We describe a canonical isomorphism of the space of global sections of L^k with a space known in conformal field theory as the ``space of conformal blocks", which is defined in terms of representations of the Lie algebra sl(r, C((z))).

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Arnaud Beauville, Yves Laszlo. 1993-09-15. Conformal blocks and generalized theta functions. https://doi.org/10.1007/bf02101707

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