Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System

Abstract

The superalgebra of observables of the rational Calogero model based on the root system R is the associative superalgebra generated by polynomials in N indeterminates, the differential-difference Dunkl's operators and the group algebra of the Coxeter group G generated by the root system R. It is shown that this superalgebra possesses Q_R supertraces, where Q_R is the number of conjugacy classes of the Coxeter group G which have no eigenvalue equal to -1.

8 pages, LATEX, misprints are corrected on p.2 and p.8