Langlands duality for finite-dimensional representations of quantum affine algebras

TL;DR

This paper establishes a duality between the q-characters of finite-dimensional representations of quantum affine algebras and their Langlands duals, introducing interpolating (q,t)-characters to bridge the two structures.

Contribution

It proves the duality for Kirillov-Reshetikhin modules and their tensor products, and introduces interpolating (q,t)-characters to connect the representations of dual algebras.

Findings

Duality between q-characters of quantum affine algebras and their Langlands duals.

Construction of interpolating (q,t)-characters that connect the dual structures.

Proof of duality for Kirillov-Reshetikhin modules and their tensor products.

Abstract

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the Kirillov-Reshetikhin modules and their irreducible tensor products. In the course of the proof we introduce and construct "interpolating (q,t)-characters" depending on two parameters which interpolate between the q-characters of a quantum affine algebra and its Langlands dual.