Virasoro Model Space

The representations of a compact Lie group G can be studied via the construction of an associated “model space”. This space has the property that when geometrically quantized its Hilbert space contains every irreducible representation of G just once. We construct an analogous space for the group Diff S1. It is naturally a complex manifold with a holomorphic, free action of Diff S1 preserving a family of pseudo-Kahler structures.All of the “good” coadjoint orbits are obtained from our space by Hamiltonian constraint reduction. We briefly discuss the connection to the work of Alekseev and Shatashvili.