Twisted self-duality of dimensionally reduced gravity and vertex operators Original Research Article

The Geroch group, isomorphic to the SL(2,R) affine Kac-Moody group, is an infinite-dimensional solution generating group of Einsteinʹs equations with two surface orthogonal commuting Killing vectors. We introduce another solution generating group for these equations, the dressing group, and discuss its connection with the Geroch group. We show that it acts transitively on a dense subset of moduli space. We use a new Lax pair expressing a twisted self-duality of this system and we study the dressing problem associated to it. We also describe how to use vertex operators to solve the reduced Einsteinʹs equations.