Publications of the Research Institute for Mathematical Sciences


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Volume 33, Issue 5, 1997, pp. 839–867
DOI: 10.2977/prims/1195145020

Finite-Dimensional Representations of Quantum Affine Algebras

Tatsuya Akasaka[1] and Masaki Kashiwara[2]

(1) International Institute for Advanced Studies, 619-0225, KYOTO, JAPAN
(2) Department of Mathematics, Kyoto University, 606-8502, KYOTO, JAPAN

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 An(1) and Cn(1).

Keywords:

Akasaka T, Kashiwara M. Finite-Dimensional Representations of Quantum Affine Algebras. Publ. Res. Inst. Math. Sci. 33 (1997), 839-867. doi: 10.2977/prims/1195145020