The (higher) Hamiltonians of (generalized) trigonometric and rational Calogero-Sutherland models by MO R-matrix

By using the integrable lattice model proposed by Maulik and Okounkov, we derive the (higher) Hamiltonians of the (generalized) trigonometric Calogero-Sutherland models. Then in terms of these (higher) Hamiltonians, we further construct certain nested structures and derive the commutative operators which coincide with the (higher) Hamiltonians of the (generalized) rational Calogero-Sutherland models.