On Schubert's Problem of Characteristics

Haibao Duan; Xuezhi Zhao

doi:10.1007/978-981-15-7451-1_4

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arXiv · 1912.10745

On Schubert's Problem of Characteristics

Haibao Duan·Xuezhi Zhao

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Abstract

The Schubert varieties on a flag manifold G/P give rise to a cell decomposition on G/P whose Kronecker duals, known as the Schubert classes on G/P, form an additive base of the integral cohomology of G/P. The Schubert's problem of characteristics asks to express a monomial in the Schubert classes as a linear combination in the Schubert basis. We present a unified formula expressing the characteristics of a flag manifold G/P as polynomials in the Cartan numbers of the group G. As application we develop a direct approach to our recent works on the Schubert presentation of the cohomology rings of flag manifolds G/P.

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Haibao Duan, Xuezhi Zhao. 2019-12-23. On Schubert's Problem of Characteristics. https://doi.org/10.1007/978-981-15-7451-1_4

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