Explicit expressions for Virasoro singular vectors

Abstract

We present two explicit expressions for generic singular vectors of type (r, s) of the Virasoro algebra. These results follow from the paper of Bauer et al. which presented recursive methods to construct the vectors. The expressions presented here generalise the results of Benoit-Saint Aubin for the type (1, s) singular vectors in two different ways: the first simply solves the recursion through the use of partitions; the second gives explicit formulae for the coefficients in a particular expansion. A Mathematica notebook is available which implements the formulae.