Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras

1999/11/30 by Edward Frenkel, Evgeny Mukhin · 3 citations
Mathematics · Physics and Astronomy · #math.QA #hep-th

paper · pdf · doi:10.1007/s002200000323

published as Commun.Math.Phys. 216 (2001) 23-57 · 35 pages, Latex

arxiv created 2000/10/06 · arxiv updated 2009/11/30

Abstract

We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from math.QA/9810055 and derive some of their corollaries. In particular, we prove that the tensor product of fundamental representations is reducible if and only if at least one of the corresponding normalized R-matrices has a pole.

Cited by

• On dominant ℓ--weights and maps between Weyl modules for quantum affine A_n
• Boundary q-characters of evaluation modules for split quantum affine symmetric pairs
• A new description of the bicrystal B(∞) and the extended crystal