Séminaire Lotharingien de Combinatoire, 86B.60 (2022), 12 pp.
Mitchell Ryan and Benjamin Solomon
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 gl(m|n).
We further generalise the Hikami-Inoue BBS
using the Kirillov-Reshetikhin crystals for gl~(m|n) devised by Kwon and Okado in 2021,
where we find similar solitonic behaviour under certain conditions.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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