Poisson involutions, spin calogero-moser systems associated with symmetric lie subalgebras and the symmetric space spin ruijsenaars-schneider models

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Abstract

We develop a general scheme to construct integrable systems starting from realizations in symmetric coboundary dynamical Lie algebroids and symmetric coboundary dynamical Poisson groupoids. The method is based on the successive use of Dirac reduction and Poisson reduction. Then we show that certain spin Calogero-Moser systems associated with symmetric Lie subalgebras can be studied in this fashion. We also consider some spin-generalized Ruisjenaars-Schneider equations which correspond to the N-soliton solutions of An (1) affine Toda field theory. In this case, we show how the equations are obtained from the Dirac reduction of some Hamiltonian system on a symmetric coboundary dynamical Poisson groupoid.

Original languageEnglish (US)
Pages (from-to)333-372
Number of pages40
JournalCommunications In Mathematical Physics
Volume265
Issue number2
DOIs
StatePublished - Jul 2006

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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