Equivalence between module categories over quiver Hecke algebras and Hernandez–Leclerc's categories in general types

Abstract

We prove in full generality that the generalized quantum affine Schur–Weyl duality functor, introduced by Kang–Kashiwara–Kim, gives an equivalence between the category of finite-dimensional modules over a quiver Hecke algebra and a certain full subcategory of finite-dimensional modules over a quantum affine algebra which is a generalization of the Hernandez–Leclerc's category CQ. This was previously proved in untwisted ADE types by Fujita using the geometry of quiver varieties, which is not applicable in general. Our proof is purely algebraic, and so can be extended uniformly to general types.