It can be shown that all Calogero-Sutherland models associated with classical A-B-C-D root spaces emerge from a single quadratic polynomial in generators of the maximal affine subalgebra of the gl(n)-algebra but unusually realized by the first order differential operators. The memory about their A-B-C-D origin is kept in coefficients of the polynomial. For the case of models related to the exceptional root spaces some unknown infinite-dimensional Lie algebras admitting finite-dimensional irreps appear.

Lie-algebraic theory allows us to construct the 'quasi-exactly-solvable' generalizations of the above Hamiltonians where a finite number of eigenstates is known exactly (algebraically). A general notion of (quasi)-exactly-solvable spectral problem is introduced.