Homology of the double and the triple loop spaces of E-6, E-7 and E-8

We study the mod p homology of the double and the triple loop spaces of exc eptional Lie groups E-6, E-7, and E-8 through the Eilenberg-Moore spectral sequence and the Serre spectral sequence using homology operations. The Boc kstein actions on them are also determined. As a result, the Eilenberg-Moor e spectral sequences of the path loop fibrations converging to H-*(Omega (2 )G; F-p) and H-*(Omega (3) C; F-p) collapse at the E-2-term for any compact simple Lie group G.