EXTENDED TODA LATTICE HIERARCHY, EXTENDED 2-MATRIX MODEL AND C=1 STRING THEORY

We show how the two-matrix model and Toda lattice hierarchy presented in a previous paper can be solved exactly: we obtain compact formulas for correlators of pure tachyonic states at every genus. We then exten d the model to incorporate a set of discrete states organized in finit e dimensional sl(2) representations. We solve also this extended model and find the correlators of the discrete states by means of the W con straints and the flow equations. Our results coincide with the ones ex isting in the literature in those cases in which particular correlator s have been explicitly calculated. We conclude that the extended two-m atrix model is a realization of the discrete states of c = 1 string th eory.