Poles of finite-dimensional representations of Yangians

• Sachin Gautam ^[1] ; Curtis Wendlandt ^[2]
  1. [1] Ohio State University

     Ohio State University

     City of Columbus, Estados Unidos

     
  2. [2] University of Saskatchewan

     University of Saskatchewan

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 1, 2023
• Idioma: inglés
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• Resumen

  • Let g be a finite-dimensional simple Lie algebra over C, and let Yℏ(g) be the Yangian of g. In this paper, we study the sets of poles of the rational currents defining the action of Yℏ(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.