Geometric approach to discrete series of unirreps for Vir.

Abstract

We want to realize the discrete series of unirreps for the Virasoro-Bott group Vir (= the central extension of Diff +( S 1)) in the space of holomorphic functions on the infinite dimensional Kähler manifold M = Diff +( S 1)/ S 1. The explicit formulae are given for the action of Vir in the space of polynomial functions in the natural complex coordinates on M.