Finite-Dimensional Representations of Quantum Affine Algebras

Abstract

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affme algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental representations is completely described by the poles of $R$-matrices. The conjecture is proved in the cases of type $A_n^{(1)}$ and $C_n^{(1)}$.