Cyclicity and R-matrices

Abstract

Let $S_1,\cdots ,S_N$ simple finite-dimensional modules of a quantum affine algebra. We prove that if $S_i\otimes S_j$ is cyclic for any $i<j$ (i.e. generated by the tensor product of the highest weight vectors), then $S_1\otimes \cdots \otimes S_N$ is cyclic. The proof is based on the study of $R$-matrices.

20 pages. This article may be seen as a generalization of arXiv:0907.3002 on which it is partially based. V2 : slight modifications, references updated. To appear in Selecta Mathematica

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