  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.
