  In this paper the quantum integrals of the Hamiltonian of the quantum
many-body problem with the interaction potential K/sinh^2(x) (Sutherland
operator) are constructed as images of higher Casimirs of the Lie algebra gl(N)
under a certain homomorphism from the center of U(gl(N)) to the algebra of
differential operators in N variables. A similar construction applied to the
affine gl(N) at the critical level k=-N defines a correspondence between higher
Sugawara operators and quantum integrals of the Hamiltonian of the quantum
many-body problem with the potential equal to constant times the Weierstrass
function. This allows one to give a new proof of the Olshanetsky-Perelomov
theorem stating that this Hamiltonian defines a completely integrable quantum
system. We also give a new expression for eigenfunctions of the quantum
integrals of the Sutherland operator as traces of intertwining operators
between certain representations of gl(N).
