The orbit method and the Virasoro extension of Diff(S): I. Orbital integrals

Using the finite dimensional example of , the universal covering of PSU(1,1), as a guide, we revisit the orbit method as it applies to , the universal central extension of . We clarify some aspects of the classification of coadjoint orbits, determine boundedness properties of the natural height function on these orbits, and calculate orbital integrals.