Supertraces on the algebra of observables of the rational Calogero model based on the classical root system

Abstract

A complete set of supertraces on the algebras of observables of the rational Calogero models with harmonic interaction based on the classical root systems of B_N, C_N and D_N types is found. These results extend the results known for the case A_N. It is shown that there exist Q independent supertraces where Q(B_N)=Q(C_N) is a number of partitions of N into a sum of positive integers and Q(D_N) is a number of partitions of N into a sum of positive integers with even number of even integers.

10 pages, LATEX

References in corpus (4)

• Exchange Operator Formalism for Integrable Systems of Particles
• Explicit Solution to the N-Body Calogero Problem
• Representations of the $S_N$-Extended Heisenberg Algebra and Relations Between Knizhnik-Zamolodchikov Equations and Quantum Calogero Model
• Supertraces on the Algebras of Observables of the Rational Calogero Model with Harmonic Potential

Cited by in corpus (1)

• Klein operator and the Numbers of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System