Equivariant cohomology of real flag manifolds |
| |
Authors: | Augustin-Liviu Mare |
| |
Affiliation: | Department of Mathematics and Statistics, University of Regina, Regina SK, S4S 0A2 Canada |
| |
Abstract: | Let P=G/K be a semisimple non-compact Riemannian symmetric space, where G=I0(P) and K=Gp is the stabilizer of p∈P. Let X be an orbit of the (isotropy) representation of K on Tp(P) (X is called a real flag manifold). Let K0⊂K be the stabilizer of a maximal flat, totally geodesic submanifold of P which contains p. We show that if all the simple root multiplicities of G/K are at least 2 then K0 is connected and the action of K0 on X is equivariantly formal. In the case when the multiplicities are equal and at least 2, we will give a purely geometric proof of a formula of Hsiang, Palais and Terng concerning H∗(X). In particular, this gives a conceptually new proof of Borel's formula for the cohomology ring of an adjoint orbit of a compact Lie group. |
| |
Keywords: | 53C50 53C35 57T15 |
本文献已被 ScienceDirect 等数据库收录! |
|