Symmetric quiver Hecke algebras and R‐matrices of quantum affine algebras III

Let Cg0 be the category of finite‐dimensional integrable modules over the quantum affine algebra Uq'(g) and let RA∞‐gmod denote the category of finite‐dimensional graded modules over the quiver Hecke algebra of type A∞. In this paper, we investigate the relationship between the categories CAN−1(1)0 and CAN−1(2)0 by constructing the generalized quantum affine Schur–Weyl duality functors F(t) from RA∞‐gmod to CAN−1(t)0(t=1,2).