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

DOI

10.1080/14029251.2013.820410How to use a DOI?

Keywords

Trace; supertrace; Cherednik algebra; algebra of observables; Calogero model

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_{W (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_{W (ℛ)} contains a Klein operator (or, equivalently, W (ℛ) ∋ − 1).

Copyright

© 2013 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - S.E. Konstein
AU  - R. Stekolshchik
PY  - 2021
DA  - 2021/01/06
TI  - Klein operator and the Number of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System
JO  - Journal of Nonlinear Mathematical Physics
SP  - 295
EP  - 308
VL  - 20
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2013.820410
DO  - 10.1080/14029251.2013.820410
ID  - Konstein2021
ER  -