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 language | English (US) |
|---|---|
| Title of host publication | Schubert calculus---Osaka 2012 |
| Publisher | Math. Soc. Japan, Tokyo |
| Pages | 475-497 |
| Number of pages | 23 |
| Volume | 71 |
| DOIs | |
| State | Published - 2016 |
Publication series
| Name | Adv. Stud. Pure Math. |
|---|---|
| Publisher | Math. 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