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

Let Uq′(g) be a twisted affine quantum group of type AN(2) or DN(2) and let g₀ be the finite-dimensional simple Lie algebra of type A_N or D_N. For a Dynkin quiver of type g₀, we define a full subcategory CQ(2) of the category of finite-dimensional integrable Uq′(g)-modules, a twisted version of the category CQ(1) introduced by Hernandez and Leclerc. Applying the general scheme of affine Schur–Weyl duality, we construct an exact faithful KLR-type duality functor FQ(2):Rep(R)→CQ(2), where Rep (R) is the category of finite-dimensional modules over the quiver Hecke algebra R of type g₀ with nilpotent actions of the generators x_k. We show that FQ(2) sends any simple object to a simple object and induces a ring isomorphism [InlineEquation not available: see fulltext.].