  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 $\La^{(1)},..., \La^{(n)}$.
