A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus
Combinatorics
2010-02-17 v3 Algebraic Geometry
Abstract
We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work of [Sch\"{u}tzenberger '77] 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 '02] and others. This rule naturally generalizes to give a conjectural root-system uniform rule for any minuscule flag variety G/P, extending [Thomas-Yong '06]. We also present analogues of results of Fomin, Haiman, Schensted and Sch\"{u}tzenberger.
Keywords
Cite
@article{arxiv.0705.2915,
title = {A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus},
author = {Hugh Thomas and Alexander Yong},
journal= {arXiv preprint arXiv:0705.2915},
year = {2010}
}
Comments
22 pages; v2 has edits to references; v3 has significant revisions/corrections, as well as new results