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arXiv · 2209.08781

Soliton cellular automata for the affine general linear Lie superalgebra

Mitchell Ryan·Benjamin Solomon
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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 $\hat{\mathfrak{gl}}{(m|n)}$ devised by Kwon and Okado (arXiv:1804.05456), where we find similar solitonic behaviour under certain conditions.

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Mitchell Ryan, Benjamin Solomon. 2022-09-19. Soliton cellular automata for the affine general linear Lie superalgebra. https://doi.org/10.1007/s00023-023-01355-5

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