  Calogero-Sutherland models associated to the Weyl groups of type A and B with
exchange terms included in the Hamiltonians systems have non-symmetric
eigenfunctions, which are products of the ground state with members of a family
of orthogonal polynomials. These polynomials can be defined and studied by
using the differential-difference operators introduced by the author in TAMS
1989 (311), 167-183. There is a study of polynomials which are invariant or
alternating for parabolic subgroups of the symmetric group. The detailed
analysis depends on using two bases of polynomials, one of which transforms
monomially under group actions and the other one is orthogonal. There are
formulas for norms and point-evaluations which are simplifications of those of
Sahi. For any parabolic subgroup of the symmetric group there is a skew
operator on polynomials which leads to evaluation at (1,1,...,1) of the
quotient of the unique skew polynomial in a given irreducible subspace by the
minimum alternating polynomial, analogously to a Weyl character formula. The
last section concerns orthogonal polynomials for the type B Weyl group with an
emphasis on the Hermite-type polynomials. A complete basis of eigenfunctions of
Yamamoto's B_N spin Calogero model is obtained by multiplying these polynomials
by the ground state.
