  We propose to parametrize the configuration space of one-dimensional quantum
systems of N identical particles by the elementary symmetric polynomials of
bosonic and fermionic coordinates. It is shown that in this parametrization the
Hamiltonians of the A_N, BC_N, B_N, C_N and D_N Calogero and Sutherland models,
as well as their supersymmetric generalizations, can be expressed -- for
arbitrary values of the coupling constants -- as quadratic polynomials in the
generators of a Borel subalgebra of the Lie algebra gl(N+1) or the Lie
superalgebra gl(N+1|N) for the supersymmetric case. These algebras are realized
by first order differential operators. This fact establishes the exact
solvability of the models according to the general definition given by one of
the authors in 1994, and implies that the Calogero and Jack-Sutherland
polynomials, as well as their supersymmetric generalizations, are related to
finite-dimensional irreducible representations of the Lie algebra gl(N+1) and
the Lie superalgebra gl(N+1|N).
