We prove that the Grothendieck rings of category CQ(t) over quantum affine algebras Uq′(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 A2n-1 (resp. Dn+1). This results provide simplicity-preserving correspondences on Langlands duality for finite-dimensional representation of quantum affine algebras, suggested by Frenkel–Hernandez.
- Combinatorial Auslander–Reiten quivers
- Langlands duality
- Longest element
- r-Cluster point
- Schur–Weyl diagram