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2008•Unpublished venueOpen access

The integral cohomology of complete flag manifolds

Haibao Duan, Xuezhi Zhao

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Abstract

Let G be an exceptional Lie group with a maximal torus T. We express the integral cohomology ring H^{\ast}(G/T) by a minimal set of Schubert classes on G/T. This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results have been applied in [DZ3] to construct the integral cohomology of a simple Lie group G in terms of Schubert classes on G/T; and in [DZ4] to determine the Steenrod operations in exceptional Lie groups.

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What this paper is about

Let G be an exceptional Lie group with a maximal torus T. We express the integral cohomology ring H^{\ast}(G/T) by a minimal set of Schubert classes on G/T. This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results have been applied in [DZ3] to construct the integral cohomology of a simple Lie group G in terms of Schubert classes on G/T; and in [DZ4] to determine the Steenrod operations in exceptional Lie groups.

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Available abstract

Let G be an exceptional Lie group with a maximal torus T. We express the integral cohomology ring H^{\ast}(G/T) by a minimal set of Schubert classes on G/T. This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results have been applied in [DZ3] to construct the integral cohomology of a simple Lie group G in terms of Schubert classes on G/T; and in [DZ4] to determine the Steenrod operations in exceptional Lie groups.

Key concepts: Mathematics, Schubert calculus, Maximal torus, Flag (linear algebra), Cohomology, Cohomology ring, Lie group, Pure mathematics

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