CHIRAL RINGS AND PHYSICAL STATES IN C-LESS-THAN-1 STRING THEORY

We show how the double cohomology of the string and Felder BRST charge s naturally leads to the ring structure of c < 1 strings. The chiral r ing is a ring of polynomials in two variables modulo an equivalence re lation of the form x(p) congruent-to y(p+1) for the (p+1, p) model. We also study the states corresponding to the edges of the conformal gri d whose inclusion is crucial for the closure of the ring. We introduce candidate operators that correspond to the observables of the matrix models. Their existence is motivated by the relation of one of the scr eening operators of the minimal model to the zero momentum dilaton.