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VOL. 71 | 2016 Cominuscule tableau combinatorics
Hugh Thomas, Alexander Yong

Editor(s) Hiroshi Naruse, Takeshi Ikeda, Mikiya Masuda, Toshiyuki Tanisaki

Abstract

We study “cominuscule tableau combinatorics” by generalizing constructions of M. Haiman, S. Fomin and M.-P. Schützenberger. In particular, we extend the dual equivalence ideas of [Haiman, 1992] to reformulate the generalized Littlewood-Richardson rule for cominuscule $G/P$ Schubert calculus from [Thomas-Yong, 2006]. We apply dual equivalence to give an alternative and independent proof of the jeu de taquin results of [Proctor, 2004] needed in our earlier work. We also extend Fomin's growth diagram description of jeu de taquin; the inherent symmetry of these diagrams leads to a generalization of Schützenberger's evacuation involution. Finally, these results are applied to give an cominuscule extension of the carton rule of [Thomas-Yong, 2008].

Information

Published: 1 January 2016
First available in Project Euclid: 4 October 2018

zbMATH: 1380.05199
MathSciNet: MR3644832

Digital Object Identifier: 10.2969/aspm/07110475

Rights: Copyright © 2016 Mathematical Society of Japan

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