Langlands duality for finite-dimensional representations of quantum affine algebras
Quantum Algebra
2011-04-20 v4 High Energy Physics - Theory
Representation Theory
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.
Keywords
Cite
@article{arxiv.0902.0447,
title = {Langlands duality for finite-dimensional representations of quantum affine algebras},
author = {Edward Frenkel and David Hernandez},
journal= {arXiv preprint arXiv:0902.0447},
year = {2011}
}
Comments
40 pages; several results and comments added. Accepted for publication in Letters in Mathematical Physics