@inbook{7143bd52ed6f4b96b59c83f392747710,
title = "Cominuscule tableau combinatorics",
abstract = "We study “cominuscule tableau combinatorics” by generalizing constructions of M. Haiman, S. Fomin and M.-P. Sch{\"u}tzenberger. 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 Sch{\"u}tzenberger's evacuation involution. Finally, these results are applied to give an cominuscule extension of the carton rule of [Thomas-Yong, 2008].",
author = "Hugh Thomas and Alexander Yong",
year = "2016",
doi = "10.2969/aspm/07110475",
language = "English (US)",
volume = "71",
series = "Adv. Stud. Pure Math.",
publisher = "Math. Soc. Japan, Tokyo",
pages = "475--497",
booktitle = "Schubert calculus---Osaka 2012",
}