Transitive actions and equivariant cohomology as an unstable \(\mathcal A^{\ast}\)-algebra (Q848768)

Given a homogeneous Kähler manifold \(X = G/H\), where \(G\) is a compact simple Lie group, the author characterizes the standard action of \(G\) on \(X\) among all topological actions by the property that the rational equivariant cohomology of \(X\) is Steenrod presentable. This means that for almost all primes \(p\), the mod \(p\) cohomology is obtained from some polynomial ring with action of the Steenrod algebra modulo an invariant ideal. The special case where \(H\) is a maximal torus was obtained earlier by the author [Math. Z. 189, 475--486 (1985; Zbl 0546.57017)].