Cluster algebra structures on module categories over quantum affine algebras

Abstract

We study monoidal categorifications of certain monoidal subcategories (Formula presented.) of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures on their Grothendieck rings (Formula presented.) are closely related to the category of finite-dimensional modules over quiver Hecke algebra of type (Formula presented.) via the generalized quantum Schur–Weyl duality functors. In particular, when the quantum affine algebra is of type (Formula presented.) or (Formula presented.), the subcategory coincides with the monoidal category (Formula presented.) introduced by Hernandez–Leclerc. As a consequence, the modules corresponding to cluster monomials are real simple modules over quantum affine algebras. © 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.