Grassmannians provide a geometrical interpretation of infinite dimensional Kac-Moody and Virasoro algebras. Here we show how to obtain, using this formulism, the values of the central charges and the conformal dimensions (weights) corresponding to the WZW and minimal models. This is achieved by suitably generalizing the procedure which gave the central charge and the conformal dimension of the b−c system. In analogy with this previous case we get a prescription to compute the correlation functions of such models on Riemann surfaces of arbitrary genus.