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

By Hugh Thomas, Alexander Yong. 2007

93 citations recorded by the source corpus.

We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work of Schutzenberger (1977) 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 Schutzenberger.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/200a599a5e726b3be6404533b83dfa19b70ddf48

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

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Citations in the corpus

k-Schur Functions and Affine Schubert Calculus (2013, methodology): “This was developed for two-row tableaux by Bergeron and Sottile [15], and by Thomas and Yong [153, 154] in the context of Hecke insertion.”
K-theory of minuscule varieties (2013, unknown): “A G ] 2 3 Ju n 20 13”