Cominuscule tableau combinatorics

Hugh Thomas, Alexander Yong

Research output: Chapter in Book/Report/Conference proceedingChapter

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].
Original languageEnglish (US)
Title of host publicationSchubert calculus---Osaka 2012
PublisherMath. Soc. Japan, Tokyo
Pages475-497
Number of pages23
Volume71
DOIs
StatePublished - 2016

Publication series

NameAdv. Stud. Pure Math.
PublisherMath. Soc. Japan, [Tokyo]

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    Thomas, H., & Yong, A. (2016). Cominuscule tableau combinatorics. In Schubert calculus---Osaka 2012 (Vol. 71, pp. 475-497). (Adv. Stud. Pure Math.). Math. Soc. Japan, Tokyo. https://doi.org/10.2969/aspm/07110475