CONFORMAL BLOCKS AND GENERALIZED THETA-FUNCTIONS

Let J U(X)(r) be the moduli space of rank r vector bundles with trivia l determinant on a Riemann surface X. This space carries a natural lin e bundle, the determinant line bundle L. We describe a canonical isomo rphism of the space of global sections of L(k) with the space of confo rmal blocks defined in terms of representations of the Lie algebra sl( r)(C((z))). It follows in particular that the dimension of H-0(J U(X)( r), L(k)) is given by the Verlinde formula.