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Liouville Integrability of a Class of Integrable Spin Calogero-Moser Systems and Exponents of Simple Lie Algebras

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Abstract

In previous work, we introduced a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter, as classified by Etingof and Varchenko for simple Lie algebras. Here the main purpose is to establish the Liouville integrability of these systems by a uniform method based on evaluating the primitive invariants of Chevalley on the Lax operators with spectral parameter. As part of our analysis, we will develop several results concerning the algebra of invariant polynomials on simple Lie algebras and their expansions.

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Author notes

  1. Zhaohu Nie

    Present address: Department of Mathematics and Statistics, Utah State University, Logan, UT, 84322, USA

Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Luen-Chau Li

  2. Department of Mathematics, Pennsylvania State University, Altoona Campus, 3000 Ivyside Park, Altoona, PA, 16601, USA

    Zhaohu Nie

Authors
  1. Luen-Chau Li
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  2. Zhaohu Nie
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Correspondence to Luen-Chau Li.

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Communicated by P. Forrester

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Li, LC., Nie, Z. Liouville Integrability of a Class of Integrable Spin Calogero-Moser Systems and Exponents of Simple Lie Algebras. Commun. Math. Phys. 308, 415–438 (2011). https://doi.org/10.1007/s00220-011-1359-x

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  • DOI: https://doi.org/10.1007/s00220-011-1359-x

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