Virasoro Representations on (Diff S1)/S1 Coadjoint Orbits

A new set of realizations of the Virasoro algebra on a bosonic Fock space are found by explicitly computing the Virasoro representations associated with coadjoint orbits of the form (Diff S1) / S1. Some progress is made in understanding the unitary structure of these representations. The characters of these representations are exactly the bosonic partition functions calculated previously by Witten using perturbative and fixed-point methods. The representations corresponding to the discrete series of unitary Virasoro representations with c <= 1 are found to be reducible in this formulation, confirming a conjecture by Aldaya and Navarro-Salas.