  The Feigin-Fuks construction of irreducible lowest-weight Virasoro
representations is reviewed using physics terminology. The procedure consists
of two steps: constructing invariants and applying them to the Fock vacuum. We
attempt to generalize this construction to the diffeomorphism algebra in higher
dimensions. The first step is straightforward, but the second is difficult, due
to the appearence of infinite Schwinger terms. This might be avoided by
imposing constraints on the fields, which should be of the recently discovered
conformal type. The resulting representations are reminiscent of quantum
gravity.
