Abstract
The box–ball system (BBS) is a cellular automaton that is an ultradiscrete analogue of the Korteweg–de Vries equation, a nonlinear PDE used to model water waves. In 2001, Hikami and Inoue generalised the BBS to the general linear Lie superalgebra gl(m|n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {gl}(m|n)$$\\end{document}. We further generalise the Hikami–Inoue BBS to column tableaux using the Kirillov–Reshetikhin crystals for gl^(m|n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{\\mathfrak {gl}}{(m|n)}$$\\end{document} devised by Kwon and Okado in 2021, where we find similar solitonic behaviour under certain conditions.
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