On unitary representations of the Virasoro algebra*

Some representations π of b of particular interest [2] are the Verma modules (V, π) = (V , π), h, c R. They are characterized by the following conditions. (i) There is a vector v = vφ = 0 in V such that Lnv = 0, n > 0, L0v = hv,Zv = cv. (ii) Let A be the set of sequences of integers k1,≥ k2 ≥ . . . ≥ kr > 0 of arbitrary length, and if α A let vα = π(L−k1) . . . π(L−kr)vφ. Then {vα|α A} is a basis of V .