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

摘要

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