Categorical relations between Langlands dual quantum affine algebras: doubly laced types

Abstract

We prove that the Grothendieck rings of category CQ(t)</mml:msubsup> over quantum affine algebras Uq</mml:msubsup>(g(t))(t=1,2) associated with each Dynkin quiver Q of finite type A2n-1 (resp. Dn+1) are isomorphic to one of the categories CQ over the Langlands dual Uq(Lg(2)) of Uq(g(2)) associated with any twisted adapted class [Q] of <mml:msub>A2n-1 (resp. <mml:msub>Dn+1). This results provide simplicity-preserving correspondences on Langlands duality for finite-dimensional representation of quantum affine algebras, suggested by Frenkel-Hernandez.