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arXiv · 1603.05014

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

David Hernandez·Bernard Leclerc
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Abstract

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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BibTeXRIS

David Hernandez, Bernard Leclerc. 2016-04-14. Cluster algebras and category O for representations of Borel subalgebras of quantum affine algebras. https://doi.org/10.2140/ant.2016.10.2015

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