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

TL;DR

This paper determines the number of supertraces on the superalgebra of observables for the rational Calogero model based on root systems, linking algebraic structures to conjugacy class properties in Coxeter groups.

Contribution

It provides a complete calculation of the supertrace counts for all irreducible root systems in the context of the rational Calogero model.

Findings

Q(R) equals the number of conjugacy classes with no eigenvalue -1

Explicit formulas for Q(R) for all irreducible root systems

Connection between supertraces and conjugacy class properties

Abstract

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