Schubert calculus and the Hopf algebra structures of exceptional Lie groups
Algebraic Topology
2014-01-14 v4 Algebraic Geometry
Abstract
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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Cite
@article{arxiv.0903.4501,
title = {Schubert calculus and the Hopf algebra structures of exceptional Lie groups},
author = {Haibao Duan and Xuezhi Zhao},
journal= {arXiv preprint arXiv:0903.4501},
year = {2014}
}
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22 pages