We show that the following two algebras are isomorphic. The first is the algebra $A_P$ of functions on the scheme of monic linear second-order differential operators on $\C$ with prescribed regular singular points at $z_1,..., z_n, \infty$, prescribed exponents $\La^{ (1)}, ..., \La^{ (n)}, \La^{ (\infty)}$ at the singular points, and having the kernel consisting of polynomials only. The second is the Bethe algebra of commuting linear operators, acting on the vector space $\Sing L_{ \La^{ (1)}} \otimes ... \otimes L_{ \La^{ (n)}}[\La^{ (\infty)}]$ of singular vectors of weight $\La^{ (\infty)}$ in the tensor product of finite dimensional polynomial $gl_2$-modules with highest weights $\La^{ (1)},..., \La^{ (n)}$.
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