E. Mukhin, V. Tarasov, A. Varchenko

May 17, 2008

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Journal

Selecta Mathematica

Abstract

Abstract.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 $$\Lambda^{(1)},\ldots,\Lambda^{(n)},\Lambda^{(\infty)}$$ 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 $$L_{\Lambda^{(1)}}\,\otimes\,\cdots\,\otimes L_{\Lambda^{(n)}}[\Lambda^{(\infty)}]$$ of singular vectors of weight Λ(∞) in the tensor product of finite-dimensional polynomial $${\mathfrak{g}}{\mathfrak{l}}_2$$-modules with highest weights $$\Lambda^{(1)},\ldots,\Lambda^{(n)}$$.