2017/10/18 by Kashiwara, Masaki, Kim, Myungho, Oh, Se-jin
#16G #16T25 #17B37 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1710.06627
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 \mathscr CB(1)n of finite-dimensional integrable modules over the quantum affine algebra of type B(1)n. It factors through the category \mathcal T2n, which is a localization of A. As a result, this functor induces a ring isomorphism from the Grothendieck ring of \mathcal T2n (ignoring the gradings) to the Grothendieck ring of a subcategory \mathscr C0B(1)n of \mathscr CB(1)n. Moreover, it induces a bijection between the classes of simple objects. Because the category \mathcal T2n is related to categories \mathscr C0_A(t)2n-1 (t=1,2) of the quantum affine algebras of type A(t)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 \mathscr C0_A(t)2n-1 and the Grothendieck ring of \mathscr C0B(1)n, which induces a bijection between the classes of simple modules.