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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 /^-matrices. The conjecture is proved in the cases of type An } and C ( n 1} . 0, IntroductionIn this paper we study finite-dimensional representations of quantum affine algebras. It is known that any finite-dimensional irreducible representation is isomorphic to the irreducible subquotient of a tensor product 0 »V(ft tv ) av containing the highest weight (Drinfeld [7]. Chari-Pressley [2]). Here V(ir t ) is the fundamental representation corresponding to the fundamental weight 7t t and a v are spectral parameters. Moreover {(TI IV \ a p )} v is uniquely determined up to permutation. This gives a parameterization of the isomorphic classes of finite-dimensional irreducible representations.However it is not known for example what is the character of those irreducible representations except the complete result for A[ 1} ([2]) and some other results due to 3,4]

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