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On Schubert’s problem of characteristics. (English) Zbl 1451.14142

Hu, Jianxun (ed.) et al., Schubert calculus and its applications in combinatorics and representation theory. Selected papers presented at the “International Festival in Schubert Calculus”, Guangzhou, China, November 6–10, 2017. Singapore: Springer. Springer Proc. Math. Stat. 332, 43-71 (2020).
Summary: 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 \(H^*(G/P)\). 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 \(G/P\).
For the entire collection see [Zbl 1445.14002].

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
55T10 Serre spectral sequences
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