Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras IV

Abstract

Let be a twisted affine quantum group of type or and let be the finite-dimensional simple Lie algebra of type or . For a Dynkin quiver of type , we define a full subcategory of the category of finite-dimensional integrable -modules, a twisted version of the category introduced by Hernandez and Leclerc. Applying the general scheme of affine Schur-Weyl duality, we construct an exact faithful KLR-type duality functor , where is the category of finite-dimensional modules over the quiver Hecke algebra R of type with nilpotent actions of the generators . We show that sends any simple object to a simple object and induces a ring isomorphism .