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

Abstract

In the Coxeter group W(R) generated by the root system R, let T(R) be the number of conjugacy classes having no eigenvalue 1 and let S(R) be the number of conjugacy classes having no eigenvalue -1. The algebra H{R) of observables of the rational Calogero model based on the root system R possesses T(R) independent traces, the same algebra considered as an associative superalgebra with respect to a certain natural parity possesses S(R) even independent supertraces and no odd trace or supertrace. The numbers T(R) and S(R) are determined for all irreducible root systems (hence for all root systems). It is shown that T(R) =< S(R), and T(R) = S(R) if and only if superalgebra H(R) contains a Klein operator (or, equivalently, W(R) containes -1).

Latex 2e, 12 pages., arXiv admin note: text overlap with arXiv:1211.6600, text corresponds to the published version

References in corpus (4)

• Lecture notes on Cherednik algebras
• Klein operator and the Numbers of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System
• Root systems and diagram calculus. I. Regular extensions of Carter diagrams and the uniqueness of conjugacy classes
• Traces on the Algebra of Observables of Rational Calogero Model based on the Root System

Cited by in corpus (8)

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• The number of independent Traces and Supertraces on the Symplectic Reflection Algebra $H_{1,\nu }(\Gamma \wr S_N)$
• Ideals generated by traces or by supertraces in the symplectic reflection algebra $H_{1,\nu }(I_2(2m+1))$
• Supertraces on queerified algebras