ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 16, 20, 83 Sawae, Ryuichi, Okayama University of Science, Japan : Hashimoto, Takashi, Tottori University, Japan An action of Virasoro algebra on the formal loop group solutions of 2d reduced Einstein equations The space of formal loop group solutions given by a linearization of the 2d reduced Einstein equations, e. g. stationary axially symmetric spacetimes, is a homogeneous space of an infinite-dimensional group G, which we call Geroch group or Hauser Group. This group represents the so-called hidden symmetry. Furthermore, there is another symmetry of the space of solutions, which comes from infinite-dimensional conformal transformations in 2 dimensional case. We discuss an action of Virasoro on the solutions, its exponentiation and a central extension related to it, from the formal loop group point of view.