Schubert calculus and the Hopf algebra structures of exceptional Lie groups

Details Schubert calculus and the Hopf algebra structures of exceptional Lie groups Schubert calculus and the Hopf algebra structures of exceptional Lie groups

2009-03-26

arxiv.org/abs/0903.4501v4

Mathematics

Algebraic Topology

22 pages

Scientific paper

Let G be an exceptional Lie group with a maximal torus T. Based on common properties in the Schubert presentation of the cohomology ring H*(G/T;F_{p}) DZ1, and concrete expressions of generalized Weyl invariants for G over F_{p}, we obtain a unified approach to the structure of H*(G;F_{p}) as a Hopf algebra over the Steenrod algebra A_{p}. The results has been applied in Du2 to determine the near--Hopf ring structure on the integral cohomology of all exceptional Lie groups.

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