THE GENUS-ZERO BOOTSTRAP OF CHIRAL VERTEX OPERATORS IN LIOUVILLE THEORY

The F and B matrices associated with Virasoro null vectors are derived in closed form by making use of the operator-approach suggested by th e Liouville theory. It is found that the entries of the fusing and bra iding matrices are not simply equal to quantum-group symbols, but invo lve additional coupling constants. Their derivation neatly follows fro m the differential equations which express the decoupling of Virasoro null vectors, combined with the general scheme of Moore and Seiberg. T he present operator formalism, contrary to the Coulomb-gas approach, a llows to study the coefficients of the operator-product algebra to all orders. Altogether the present work, and a subsequent article, give t he concrete realization of Moore and Seiberg's scheme that describes t he chiral operator-algebra of two-dimensional gravity and minimal mode ls.