Abstract
We give the extension of the free field representation of SU(2) k WZNW model conformal blocks to an arbitrary Riemann surface. In particular, we avoid the problems associated with the vertex corresponding to the dual of a given representation - namely that it does not transform as the appropriate highest weight field of the current algebra - in a way allowing the sewing procedure to be applied. After analysing the two-point function on the torus as an illustration of some of the subtleties in this free field representation, we go on to give the genus-two characters as an application.
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