2019年1月1日
Jeu de taquin, uniqueness of rectification and ultradiscrete KP
Journal of Integrable Systems
- 巻
- 4
- 号
- 1
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1093/integr/xyz012
- 出版者・発行元
- Oxford University Press (OUP)
<title>Abstract</title>
In this article, 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.
In this article, 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.
- リンク情報
- ID情報
-
- DOI : 10.1093/integr/xyz012
- ISSN : 2058-5985
- eISSN : 2058-5985
- ORCIDのPut Code : 67195065