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A combinatorial rule for (co)minuscule Schubert calculus

Hugh Thomas·Alexander Yong
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Abstract

We prove a root system uniform, concise combinatorial rule for Schubert calculus of_minuscule_ and_cominuscule_ flag manifolds G/P (the latter are also known as "compact Hermitian symmetric spaces"). We connect this geometry to the poset combinatorics of [Proctor '04], thereby giving a generalization of the [Schützenberger `77]_jeu de taquin_ formulation of the Littlewood-Richardson rule that computes the intersection numbers of Grassmannian Schubert varieties. Our proof introduces_cominuscule recursions_, a general technique to relate the numbers for different Lie types. A discussion about connections of our rule to (geometric) representation theory is also briefly entertained.

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BibTeXRIS

Hugh Thomas, Alexander Yong. 2006-09-07. A combinatorial rule for (co)minuscule Schubert calculus. https://arxiv.org/abs/math/0608276

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