SUPERTRACES ON THE ALGEBRAS OF OBSERVABLES OF THE RATIONAL CALOGERO MODEL WITH HARMONIC POTENTIAL

We define a complete set of supertraces on the algebra SHN(nu), the al gebra of observables of the N-body rational Calogero model with harmon ic interaction. This result extends the previously known results for t he simplest cases of N = 1 and N = 2 to arbitrary N. It is shown that SHN(nu) admits q(N) independent supertraces, where q(N) is a number of partitions of N into a sum of odd positive integers, so that q(N)>1 f or N greater than or equal to 3. Some consequences of the existence of several independent supertraces of SHN(nu) are discussed, such as the existence of ideals in associated W-infinity-type Lie superalgebras. (C) 1996 American Institute of Physics.