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

Thomas, Hugh; Yong, Alexander

doi:10.2140/ant.2009.3.121

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

Hugh Thomas and Alexander Yong

Vol. 3 (2009), No. 2, 121–148

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 $G ∕ P$ , extending recent work of Thomas and Yong. We also present analogues of results of Fomin, Haiman, Schensted and Schützenberger.

Keywords

Schubert calculus, K-theory, jeu de taquin

Mathematical Subject Classification 2000

Primary: 05E10

Secondary: 14M15

Milestones

Received: 4 November 2007

Revised: 17 September 2008

Accepted: 29 November 2008

Published: 15 March 2009

Authors

Hugh Thomas
Tilley Hall 418 Department of Mathematics and Statistics University of New Brunswick Fredericton, New Brunswick E3B 5A3 Canada
http://www.math.unb.ca/~hugh/
Alexander Yong
1409 W. Green Street Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801 United States
http://www.math.uiuc.edu/~ayong

Vol. 3, No. 2, 2009