A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus

Details A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus

2007-05-21

arxiv.org/abs/0705.2915v3

Algebra Number Theory 3 (2009), no. 2, 121--148.

Mathematics

Combinatorics

22 pages; v2 has edits to references; v3 has significant revisions/corrections, as well as new results

Scientific paper

We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work of [Sch\"{u}tzenberger '77] 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 '02] and others. This rule naturally generalizes to give a conjectural root-system uniform rule for any minuscule flag variety G/P, extending [Thomas-Yong '06]. We also present analogues of results of Fomin, Haiman, Schensted and Sch\"{u}tzenberger.

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