Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel

• E. Mukhin ^[1] ; V. Tarasov ^[1] ; A. Varchenko ^[2]
  1. [1] Purdue University

     Purdue University

     Township of Wabash, Estados Unidos

     
  2. [2] University of North Carolina at Chapel Hill

     University of North Carolina at Chapel Hill

     Township of Chapel Hill, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 14, Nº. 1, 2008, págs. 121-144
• Idioma: inglés
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• Resumen

  • We show that the algebra of functions on the scheme of monic linear second-order ordinary differential operators with prescribed n + 1 regular singular points, prescribed exponents Λ(1),…,Λ(n),Λ(∞) at the singular points, and having the kernel consisting of polynomials only, is isomorphic to the Bethe algebra of the Gaudin model acting on the vector space Sing LΛ(1)⊗⋯⊗LΛ(n)[Λ(∞)] of singular vectors of weight Λ(∞) in the tensor product of finite-dimensional polynomial gl2 -modules with highest weights Λ(1),…,Λ(n) .