Braid group actions and tensor products (Q2782261)

This paper gives a sufficient condition for the tensor product of irreducible finite-dimensional representations of quantum affine algebras to be cyclic. The condition is that the action of the braid group on the \(n\)-tuple \(\pi\) of polynomials yields polynomials in ``general position'' with respect to \(\pi\). This generalizes the condition for the \(\mathfrak{sl}_2\) case. It also establishes a conjecture stated in \textit{G. Hatayama} et al., Contemp. Math. 248, 243-291 (1999; Zbl 1032.81015), and Kashiwara.