Volume 20, Issue 2, May 2013, Pages 271 - 294
Traces on the Algebra of Observables of the Rational CalogeroModel Based on the Root System
Received 2 December 2012, Accepted 1 June 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.820403How to use a DOI?
- Keywords
- Calogero model; Cherednik algebra; trace, supertrace
- Abstract
It is shown that HW (ℛ) (η), the algebra of observables of the rational Calogero model based on the root system ℛ ⊂ ℝN, has Tℛ independent traces, where Tℛ is the number of conjugacy classes of elements without eigenvalue 1 belonging to the Coxeter group W (ℛ) ⊂ End ℝN generated by the root system ℛ.
Simultaneously, we reproduce an known result: the algebra HW (ℛ) (η), considered as a superalgebra with a natural parity, has STℛ independent supertraces, where STℛ is the number of conjugacy classes of elements without eigenvalue −1 belonging to W (ℛ).
- 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/).
Cite this article
TY - JOUR AU - S.E. Konstein AU - I.V. Tyutin PY - 2021 DA - 2021/01/06 TI - Traces on the Algebra of Observables of the Rational CalogeroModel Based on the Root System JO - Journal of Nonlinear Mathematical Physics SP - 271 EP - 294 VL - 20 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.820403 DO - 10.1080/14029251.2013.820403 ID - Konstein2021 ER -