Soliton cellular automata for the affine general linear Lie superalgebra

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 $\mathfrak{g}\mathfrak{l}(m\mathrm{\mid }n)$. We further generalise the Hikami–Inoue BBS to column tableaux using the Kirillov–Reshetikhin crystals for $\widehat{\mathfrak{g}\mathfrak{l}}(m\mathrm{\mid }n)$ devised by Kwon and Okado (arXiv:1804.05456), where we find similar solitonic behaviour under certain conditions.