Cluster algebra structures on module categories over quantum affine algebras

We study monoidal categorifications of certain subcategories C J $\mathcal {C}_J$ finite-dimensional modules over quantum affine algebras, whose cluster algebra structures on their Grothendieck rings K ( ) $K(\mathcal {C}_J)$ are closely related to the category quiver Hecke type A ∞ $A_\infty$ via generalized Schur–Weyl duality functors. In particular, when is $A$ or B $B$ , subcategory coincides with g 0 {C}_{\mathfrak {g}}^0$ introduced by Hernandez–Leclerc. As a consequence, corresponding monomials real simple algebras.