Vol. 3, No. 2, 2009

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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

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.

Schubert calculus, K-theory, jeu de taquin
Mathematical Subject Classification 2000
Primary: 05E10
Secondary: 14M15
Received: 4 November 2007
Revised: 17 September 2008
Accepted: 29 November 2008
Published: 15 March 2009
Hugh Thomas
Tilley Hall 418
Department of Mathematics and Statistics
University of New Brunswick
Fredericton, New Brunswick E3B 5A3
Alexander Yong
1409 W. Green Street
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801
United States