|The Virasoro algebra is an infinite dimensional Lie algebra which is a one dimensional central extension of the Lie algebra of (polynomial) vector fields in the punctured complex line. From the point of view of mathematical physics (which will not be developed in the talk), this is the Lie algebra of infinitesimal symmetries for the (bosonic) string theory. From the mathematical point of view, this is a unique simple Lie algebra of polynomial growth which does not belong to two major classes of such Lie algebras: Cartan algebras of vector fields and Kac-Moody algebras. Likewise, the representation theory of the Virasoro algebra is amazingly different from other representation theories.
In the talk, I will present some results, mainly, from the works of
the late 80-ies due to Boris Feigin and myself. I will not use any
specific technique of the representation theory: the talk will be
addressed to a broad mathematical audience.|