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

E. Mukhin, V. Tarasov, Alexander Varchenko

• 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) .