Cohomology operations in the space of loops on the exceptional Lie group \(E_6\) (Q1766210)

The author computes the action of the dual of the Steenrod algebra \({\mathcal A}_p\) on the homology \(H_*(\Omega E_6;\mathbb{Z}/p\mathbb{Z})\) for \(p= 2,3\) where \(E_6\) denotes the compact 1-connected exceptional Lie group. In the course of computation he also determines the action of \({\mathcal A}_3\) on the cohomology \(H^*(E_6/T; \mathbb{Z}/3\mathbb{Z})\) where \(T\) is a maximal torus of \(E_6\).