Infinitesimal Baecklund transformations and Kac--Moody algebras in general relativity

Infinitesimal Baecklund transformations are found for the problem of classical general relativity in d dimensions, which by dimensional reduction may be interpreted as gravitation interacting with several Maxwell and scalar fields. The transformations are constructed in terms of the solution of a linear system whose integrability condition yields the original field equations. The Kac--Moody algebra, which generates those transformations, is analyzed