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

摘要

Let $\mathcal{O}$ be the category of representations of the Borel subalgebraof a quantum affine algebra introduced by Jimbo and the first author. We showthat the Grothendieck ring of a certain monoidal subcategory of $\mathcal{O}$has the structure of a cluster algebra of infinite rank, with an initial seedconsisting of prefundamental representations. In particular, the celebratedBaxter relations for the 6-vertex model get interpreted as Fomin-Zelevinskymutation relations.