SUPERTRACES ON THE ALGEBRAS OF OBSERVABLES OF THE RATIONAL CALOGERO MODELS RELATED TO CLASSICAL ROOT SYSTEMS

We define a complete set of supertraces on the algebra H-W(R)(nu), the algebra of observables of the rational Calogero model with a harmonic interaction based on the B-N, C-N, and D-N types of the classical roo t systems R. These results extend those known for the case A(N-1). It is Shown that H-W(R)(nu) admits q(R) independent supertraces, where q( B-N) = q(C-N) is the number of partitions of N into a sum of positive integers and q(D-N) is the number of partitions of N into a sum of pos itive integers with an even number of even integers.