Algebra & Number Theory

A jeu de taquin theory for increasing tableaux, with applications to {\textsl K}\hskip-2pt-theoretic Schubert calculus

Hugh Thomas and Alexander Yong

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We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work of Schützenberger (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 GP, extending recent work of Thomas and Yong. We also present analogues of results of Fomin, Haiman, Schensted and Schützenberger.

Article information

Algebra Number Theory, Volume 3, Number 2 (2009), 121-148.

Received: 4 November 2007
Revised: 17 September 2008
Accepted: 29 November 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Primary: 05E10: Combinatorial aspects of representation theory [See also 20C30]
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]

Schubert calculus K-theory jeu de taquin


Thomas, Hugh; Yong, Alexander. A jeu de taquin theory for increasing tableaux, with applications to {\textsl K}\hskip-2pt-theoretic Schubert calculus. Algebra Number Theory 3 (2009), no. 2, 121--148. doi:10.2140/ant.2009.3.121.

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