Traces on the Algebra of Observables of Rational Calogero Model based on the Root System

It is shown that H_R(\nu), the algebra of observables of the rational Calogero model based on the root system R, possesses T® independent traces, where T® is the number of conjugacy classes of elements without eigenvalue 1 belonging to the Coxeter group W® generated by the root system R. Simultaneously, we reproduced an older result: the algebra H_R(\nu), considered as a superalgebra with a natural parity, possesses ST® independent supertraces, where ST® is the number of conjugacy classes of elements without eigenvalue -1 belonging to W®.