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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.08781 |
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| _version_ | 1866929263121268736 |
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| author | Ryan, Mitchell Solomon, Benjamin |
| author_facet | Ryan, Mitchell Solomon, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08781 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Soliton cellular automata for the affine general linear Lie superalgebra Ryan, Mitchell Solomon, Benjamin Exactly Solvable and Integrable Systems Mathematical Physics Combinatorics 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. |
| title | Soliton cellular automata for the affine general linear Lie superalgebra |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Combinatorics |
| url | https://arxiv.org/abs/2209.08781 |