CONTINUOUS SPINS IN 2D GRAVITY - CHIRAL VERTEX OPERATORS AND LOCAL-FIELDS

We construct the exponentials of the Liouville field with continuous p owers within the operator approach. Their chiral decomposition is real ized using the explicit Coulomb-gas operators we introduced earlier. F rom the quantum group viewpoint, they are related to semi-infinite hig hest- or lowest-weight representations with continuous spins. The Liou ville field itself is defined, and the canonical commutation relations are verified, as well as the validity of the quantum Liouville field equations. In a second part, both screening charges are considered. Th e braiding of the chiral components is derived and shown to agree with the ansatz of a parallel paper of Gervais and Roussel: for continuous spins the quantum group structure U-q(s1(2)).OU(q)S1(2)) is a nontriv ial extension of U-q(sl(2)) and U(q)s1(2)). We construct the correspon ding generalized exponentials and the generalized Liouville field.