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Coherent presentations of super plactic monoids of type A by insertions
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In this paper, we study by rewriting methods the presentations of the super plactic monoid of type A which is related to the representations of the general linear Lie superalgebra. We construct a convergent presentation of this monoid whose generators are super columns and whose rules are defined by insertions on super tableaux over a signed alphabet. We extend this presentation into a coherent one whose syzygies are defined as relations among insertion algorithms. Finally, we reduce this coherent presentation to a Tietze equivalent one over the initial signed alphabet. Such coherent presentations are used for representations of super plactic monoids by describing their actions on categories.
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