Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant cohomology of real flag manifolds   Let $P=G/K$ be a semisimple non-compact Riemannian symmetric space, where
$G=I_0(P)$ and $K=G_p$ is the stabilizer of $p\in P$. Let $X$ be an orbit of
the (isotropy) representation of $K$ on $T_p(P)$ ($X$ is called a real flag
manifold). Let $K_0\subset K$ 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 $K_0$ is connected and the
action of $K_0$ 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.

15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph