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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.

##### MSC:
 05E10 Combinatorial aspects of representation theory 14M15 Grassmannians, Schubert varieties, flag manifolds
##### Keywords:
Schubert calculus; $$K$$-theory; jeu de taquin
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