Jeu de taquin, uniqueness of rectification, and ultradiscrete KP
Abstract
In this paper, we study tropical-theoretic aspects of the ``rectification algorithm'' on skew Young tableaux. It is shown that the algorithm is interpreted as a time evolution of some tropical integrable system. By using this fact, we construct a new combinatorial map that is essentially equivalent to the rectification algorithm. Some of properties of the rectification can be seen more clearly via this map. For example, the uniqueness of a rectification boils down to an easy combinatorial problem. Our method is mainly based on the two previous researches: the theory of geometric tableaux by Noumi-Yamada, and the study on the relationship between jeu de taquin slides and the ultradiscrete KP equation by Mikami and Katayama-Kakei.
Keywords
Cite
@article{arxiv.1803.01208,
title = {Jeu de taquin, uniqueness of rectification, and ultradiscrete KP},
author = {Shinsuke Iwao},
journal= {arXiv preprint arXiv:1803.01208},
year = {2020}
}
Comments
22pages, 1 figure. Most part of this paper (except for Sections 5.4, 5.5, and 6) is an English translation of the author's unpublished manuscript "S. Iwao, Jeu de taquin, uniqueness of a rectification, and ultradiscrete KP'' written in Japanese