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In the Coxeter group W(R) generated by the root system R, let Q(R) be thenumber of conjugacy classes having no eigenvalue -1. The superalgebra ofobservables of the rational Calogero model based on the root system R possessesQ(R) supertraces. The numbers Q(R) are determined for all irreducible rootsystems (hence for all root systems).

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