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 B n ( 1 )of finite‐dimensional integrable modules over the quantum affine algebra of type B n ( 1 ) . It factors through the category T 2 n , which is a localization of A . As a result, this functor induces a ring isomorphism from the Grothendieck ring of T 2 n(ignoring the gradings) to the Grothendieck ring of a subcategory C B n ( 1 ) 0 of C B n ( 1 ). Moreover, it induces a bijection between the classes of simple objects. Because the category T 2 nis related to categories C A 2 n − 1 ( t ) 0( t = 1 , 2 ) of the quantum affine algebras of type A 2 n − 1 ( t ) , 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 C A 2 n − 1 ( t ) 0 and the Grothendieck ring of C B n ( 1 ) 0 , which induces a bijection between the classes of simple modules.