A combinatorial rule for (co)minuscule Schubert calculus |
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Authors: | Hugh Thomas |
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Affiliation: | a Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada b Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States |
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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, thereby giving a generalization of Schützenberger's 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. |
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Keywords: | Schubert calculus Littlewood-Richardson rules Minuscule Schubert varieties Algebraic combinatorics |
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