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Article Dans Une Revue Algebra & Number Theory Année : 2016

Cluster algebras and category O for representations of Borel subalgebras of quantum affine algebras

Résumé

Let $\mathcal{O}$ be the category of representations of the Borel subalgebra of a quantum affine algebra introduced by Jimbo and the first author. We show that the Grothendieck ring of a certain monoidal subcategory of $\mathcal{O}$ has the structure of a cluster algebra of infinite rank, with an initial seed consisting of prefundamental representations. In particular, the celebrated Baxter relations for the 6-vertex model get interpreted as Fomin-Zelevinsky mutation relations.
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hal-01767345 , version 1 (27-02-2024)

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David Hernandez, Bernard Leclerc. Cluster algebras and category O for representations of Borel subalgebras of quantum affine algebras. Algebra & Number Theory, 2016, 10 (9), pp.2015 - 2052. ⟨10.2140/ant.2016.10.2015⟩. ⟨hal-01767345⟩
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