Kono, Akira; Ishitoya, Kiminao Squaring operations in mod 2 cohomology of quotients of compact Lie groups by maximal tori. (English) Zbl 0656.57025 Algebraic topology, Proc. Symp., Barcelona/Spain 1986, Lect. Notes Math. 1298, 192-206 (1987). [For the entire collection see Zbl 0626.00023.] The authors complete the determination of the mod 2 cohomology of G/T, where G is a compact, 1-connected simple Lie group and T is a maximal torus, by considering the cases of \(E_ 7/T\) and \(E_ 8/T\). In addition the action of the Steenrod algebra is determined in all cases. The proofs draw on the previous literature and the calculations rely on a careful choice of bases for \(H^ 2(BT,Z)\) in place of the usual fundamental weights. Reviewer: J.Hubbuck Cited in 1 ReviewCited in 4 Documents MSC: 57T15 Homology and cohomology of homogeneous spaces of Lie groups 57T10 Homology and cohomology of Lie groups 55R40 Homology of classifying spaces and characteristic classes in algebraic topology Keywords:mod 2 cohomology of homogeneous spaces; compact Lie group modulo a maximal torus; exceptional Lie groups; Steenrod squares; action of the Steenrod algebra Citations:Zbl 0626.00023 PDFBibTeX XML