  Talk presented by J.L. Petersen at the 29th Symposium Ahrenshop, Buckow
August 29-September 2, 1995. A presentation is given of the free field
realization relevant to SL(2) WZW theories with a Hilbert space based on
admissible representations. It is known that this implies the presence of two
screening charges, one involving a fractional power of a free field. We develop
the use of fractional calculus for treating in general such cases. We derive
explicit integral representations of $N$-point conformal blocks. We show that
they satisfy the Knizhnik-Zamolodchikov equations and we prove how they are
related to minimal conformal blocks via a formulation of hamiltonian reduction
advocated by Furlan, Ganchev, Paunov and Petkova.
