Infinite-Dimensional Geometry of the Universal Deformation of the Complex Disk

Abstract

The universal deformation of the complex disk is studied from the viewpoint of infinite-dimensional geometry. The structure of a subsymmetric space on the universal deformation is described. The foliation of the universal deformation by subsymmetry mirrors is shown to determine a real polarization. The subject of the paper maybe of interest to specialists in algebraic geometry and representation theory as well as to researchers dealing with mathematical problems of modern quantum field theory. Contents. I. The infinite-dimensional geometry of the flag manifold of the Virasoro-Bott group (the base of the universal deformation of the complex disk). II. The infinite-dimensional geometry of the skeleton of the flag manifold of the Virasoro-Bott group. III. The infinite-dimensional geometry of the universal deformation of the complex disk.