Abstract
Let 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 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.
Citation
David Hernandez. Bernard Leclerc. "Cluster algebras and category $\mathscr{O}$ for representations of Borel subalgebras of quantum affine algebras." Algebra Number Theory 10 (9) 2015 - 2052, 2016. https://doi.org/10.2140/ant.2016.10.2015
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