The Number of Supertraces on the Superalgebra of Observables of Rational   Calogero Model based on the Root System
  In the Coxeter group W(R) generated by the root system R, let Q(R) be the number of conjugacy classes having no eigenvalue -1. The superalgebra of observables of the rational Calogero model based on the root system R possesses Q(R) supertraces. The numbers Q(R) are determined for all irreducible root systems (hence for all root systems). 
S. E. Konstein and R. Stekolshchik