The equivariant cohomology of isotropy actions on symmetric spaces (Q418683)

Let \((G,K)\) be a Riemannian symmetric pair of the compact type such that \(G\) and \(K\) are connected Lie groups. The author shows that the \(K\)-action on the symmetric space \(G/K\) by left translation is equivariantly formal. Certain results in this direction were previously known for example in the case of \(K\) and \(G\) having equal rank and for symmetric spaces of ``type II'', that is symmetric spaces that are compact Lie groups.