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We show that the following two algebras are isomorphic. The first is thealgebra $A_P$ of functions on the scheme of monic linear second-orderdifferential 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 ofpolynomials only. The second is the Bethe algebra of commuting linearoperators, acting on the vector space $\Sing L_{\La^{(1)}} \otimes ... \otimesL_{\La^{(n)}}[\La^{(\infty)}]$ of singular vectors of weight $\La^{(\infty)}$in the tensor product of finite dimensional polynomial $gl_2$-modules withhighest weights $\La^{(1)},..., \La^{(n)}$.

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