Rational homotopy theory of flag manifolds

Source abstract

Let $G/P$ be a flag manifold with $G$ simple. We determine the rational homotopy groups $π_{\ast }(G/P)\otimes \mathbb{Q}$ and describe the rational cohomology ring $H^{\ast }(G/P;\mathbb{Q})$ in terms of the rational homotopy types $\mathcal{F}_{G}$ and $\mathcal{F}_{P}$ of $G$ and $$, respectively. The proof is based on the restrictions of basic Weyl invariants of $G$ to suitable simple factors of $P$.