Poles of finite-dimensional representations of Yangians

Let g be a finite-dimensional simple Lie algebra over C, and let Y-h(g) be the Yangian of g. In this paper, we study the sets of poles of the rational currents defining the action of Y-h(g) on an arbitrary finite-dimensional vector space V. Using a weak, rational version of Frenkel and Hernandez' Baxter polynomiality, we obtain a uniform description of these sets in terms of the Drinfeld polynomials encoding the composition factors of V and the inverse of the q-Cartan matrix of g. We then apply this description to obtain a concrete set of sufficient conditions for the cyclicity and simplicity of the tensor product of any two irreducible representations, and to classify the finite-dimensional irreducible representations of the Yangian double.