[en] In this paper, the authors study c < 1 matter coupled to gravity in the Coulomb gas formalism using the double cohomology of the string BRST and Felder BRST charges. The authors find that states outside the primary conformal grid are related to the states of nonzero ghost number by means of descent equations given by the double cohomology. Some aspects of the Virasoro structure of the Liouville-Fock space are studied. As a consequence, states of nonzero ghost number are easily constructed by solving these descent equations. This enables the authors to map ghost number conserving correlation functions involving nonzero ghost number states into those involving states outside the primary conformal grid