Summary: Journal of Algebra 269 (2003) 480­491
www.elsevier.com/locate/jalgebra
Quasi-potentials and Kähler­Einstein metrics
on flag manifolds, II
Hassan Azad a,
and Indranil Biswas b
a Department of Mathematical Sciences, King Fahd University, Dhahran 31261, Saudi Arabia
b School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Received 5 May 2002
Communicated by J.T. Stafford
Abstract
For a homogeneous space G/P, where P is a parabolic subgroup of a complex semisimple
group G, an explicit Kähler­Einstein 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 Kähler­Einstein metric, thus enabling
us to compute volume for this metric and for all Kählerian metrics on G/P invariant under the action
of a maximal compact subgroup of G.
2003 Elsevier Inc. All rights reserved.
1. Introduction
Let G be a complex reductive group, P a parabolic subgroup of G and K a maximal

Source: Azad, Hassan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals

Collections: Mathematics