  Let W be a finite Coxeter group in a Euclidean vector space V, and m a
W-invariant Z_+-valued function on the set of reflections in W. Chalyh and
Veselov introduced in an interesting algebra Q_m, called the algebra of
m-quasiinvariants for W. This is the algebra of quantum integrals of the
rational Calogero-Moser system with coupling constants m. In a recent paper
math-ph/0105014, Feigin and Veselov proposed a number of interesting
conjectures concerning the structure of Q_m, and verified them for dihedral
groups and constant functions m. Our goal is to prove some of these conjectures
in the general case.
