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

Mathematics – Quantum Algebra

Scientific paper

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35 pages, Latex

Scientific paper

10.1007/s002200000323

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.

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