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2009 A jeu de taquin theory for increasing tableaux, with applications to {\textsl K}\hskip-2pt-theoretic Schubert calculus
Hugh Thomas, Alexander Yong
Algebra Number Theory 3(2): 121-148 (2009). DOI: 10.2140/ant.2009.3.121

Abstract

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.

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Hugh Thomas. Alexander Yong. "A jeu de taquin theory for increasing tableaux, with applications to {\textsl K}\hskip-2pt-theoretic Schubert calculus." Algebra Number Theory 3 (2) 121 - 148, 2009. https://doi.org/10.2140/ant.2009.3.121

Information

Received: 4 November 2007; Revised: 17 September 2008; Accepted: 29 November 2008; Published: 2009
First available in Project Euclid: 20 December 2017

MathSciNet: MR2491941
Digital Object Identifier: 10.2140/ant.2009.3.121

Subjects:
Primary: 05E10
Secondary: 14M15

Keywords: jeu de taquin , ‎K-theory , Schubert calculus

Rights: Copyright © 2009 Mathematical Sciences Publishers

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