Monoidal categories of modules over quantum affine algebras of type A and B

We construct an exact tensor functor from the category A of finite-dimensional graded modules over the quiver Hecke algebra of type A∞ to the category C_Bn(1) of finite-dimensional integrable modules over the quantum affine algebra of type B_n ¹. It factors through the category T_2n, which is a localization of A. As a result, this functor induces a ring isomorphism from the Grothendieck ring of T_2n (ignoring the gradings) to the Grothendieck ring of a subcategory C⁰ _Bn(1) of C_Bn(1). Moreover, it induces a bijection between the classes of simple objects. Because the category T_2n is related to categories (Formula presented.) (t = 1, 2) of the quantum affine algebras of type A⁽¹⁾ _2n-1, we obtain an interesting connection between those categories of modules over quantum affine algebras of type A and type B. Namely, for each t = 1, 2, there exists an isomorphism between the Grothendieck ring of C⁰ _Bn(1) and the Grothendieck ring of (Formula presented.), which induces a bijection between the classes of simple modules.