Double centralizers of unipotent elements in simple algebraic groups of type E7E7 and E8E8

This article addresses questions about the double centralizer CG(CG(u))=Z(CG(u))CG(CG(u))=Z(CG(u)) of unipotent elements u in simple algebraic groups G   of type E7E7 and E8E8 defined over algebraically closed fields of bad characteristic. We use the method developed in [14] to determine Z(CG(u))∘Z(CG(u))∘, deduce its dimension and recognize if it is an overgroup for u  . The method used requires explicit representatives of the component group of CG(u)CG(u) which we produce in all cases. This article extends the results of [14] to all exceptional type groups.