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A jeu de taquin theory for increasing tableaux, with application to \(K\)-theoretic Schubert calculus. (English) Zbl 1229.05285
Summary: We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work of M.-P. Schützenberger [Lect. Notes Math. 579, 59–113 (1977; Zbl 0398.05011)] for standard Young tableaux. We apply this to give a new combinatorial rule for the \(K\)-theory Schubert calculus of Grassmannians via \(K\)-theoretic jeu de taquin, providing an alternative to the rules of Buch and others. This rule naturally generalizes to give a conjectural root-system uniform rule for any minuscule flag variety \(G/P\), extending recent work of Thomas and Yong. We also present analogues of results of Fomin, Haiman, Schensted and Schützenberger.

05E10 Combinatorial aspects of representation theory
14M15 Grassmannians, Schubert varieties, flag manifolds
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