Quasi-potentials and Kahler-Einstein metrics on flag manifolds, II

Abstract

For a homogeneous space G/P, where P is a parabolic subgroup of a complex semisimple group G, an explicit Kahler-Einstein metric on it is constructed. The Einstein constant for the metric is 1. Therefore, the intersection number of the first Chern class of the holomorphic tangent bundle of G/P coincides with the volume of G/P with respect to this Kahler-Einstein metric, thus enabling us to compute volume for this metric and for all Kahlerian metrics on G/P invariant under the action of a maximal compact subgroup of G.