Supertraces on the algebras of observables of the rational calogero models related to classical root systems

Abstract

We define a complete set of supertraces on the algebra HW(R)(v), the algebra of observables of the rational Calogero model with a harmonic interaction based on the BN, CN, and DN types of the classical root systems R. These results extend those known for the case AN−1. It is shown that HW(R)(v) admits q(R) independent supertraces, where q(BN)=q(CN) is the number of partitions of N into a sum of positive integers and q(DN) is the number of partitions of N into a sum of positive integers with an even number of even integers.