Classical r-matrices and the Feigin-Odesskii algebra via Hamiltonian and Poisson reductions

H W Braden, V A Dolgushev, M A Olshanetsky, A V Zotov

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We present a formula for a classical r-matrix of an integrable system obtained by Hamiltonian reduction of some free field theories using pure gauge symmetries. The framework of the reduction is restricted only by the assumption that the respective gauge transformations are Lie group ones. Our formula is in terms of Dirac brackets, and some new observations on these brackets are made. We apply our method to derive a classical r-matrix for the elliptic Calogero Moser system with spin starting from the Higgs bundle over an elliptic curve with marked points. In the paper, we also derive a classical Feigin-Odesskii algebra by a Poisson reduction of some modification of the Higgs bundle over an elliptic curve. This allows us to include integrable lattice models in a Hitchin-type construction.

Original languageEnglish
Pages (from-to)6979-7000
Number of pages22
JournalJournal of Physics A: Mathematical and General
Volume36
Issue number25
Publication statusPublished - 27 Jun 2003

Keywords / Materials (for Non-textual outputs)

  • AFFINE LIE-ALGEBRAS
  • CALOGERO-MOSER MODELS
  • YANG-BAXTER EQUATION
  • RIEMANN SURFACES
  • ELLIPTIC-CURVES
  • HIGHEST WEIGHT
  • SYSTEMS
  • MODULES
  • BUNDLES

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