Vol. 3, No. 2, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 10, 1767–1943
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
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
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.

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