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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