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

Abstract

We prove that the Grothendieck rings of category ${\mathcal{C}}_Q^{(t)}$ over quantum affine algebras $U_q'(\g^{(t)})$ $(t=1,2)$ associated to each Dynkin quiver $Q$ of finite type $A_{2n-1}$ (resp. $D_{n+1}$) is isomorphic to one of category $\mathcal{C}_{\mQ}$ over the Langlands dual $U_q'({^L}\g^{(2)})$ of $U_q'(\g^{(2)})$ associated to any twisted adapted class $[\mQ]$ of $A_{2n-1}$ (resp. $D_{n+1}$). This results provide partial answers of conjectures of Frenkel-Hernandez on Langlands duality for finite-dimensional representation of quantum affine algebras.

References in corpus (2)

• 2-Kac-Moody algebras
• Monoidal categorification of cluster algebras II

Cited by in corpus (1)

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