Soliton cellular automata for the affine general linear Lie superalgebra

Abstract

The box-ball system (BBS) is a cellular automaton that is an ultradiscrete analogue of the Korteweg--de Vries equation, a non-linear PDE used to model water waves. In 2001, Hikami and Inoue generalised the BBS to the general linear Lie superalgebra $\mathfrak{gl}(m|n)$. We further generalise the Hikami--Inoue BBS to column tableaux using the Kirillov--Reshetikhin crystals for $\widehat{\mathfrak{gl}}(m|n)$ devised by Kwon and Okado (arXiv:1804.05456), where we find similar solitonic behaviour under certain conditions.

51 pages, 0 figures

References in corpus (4)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• Soliton Cellular Automata Associated With Crystal Bases
• Energy Functions in Box Ball Systems
• Box ball system associated with antisymmetric tensor crystals