Duality between the trigonometric BCn Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system

L. Fehér, T. F. Görbe

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We present a new case of duality between integrable many-body systems, where two systems live on the action-angle phase spaces of each other in such a way that the action variables of each system serve as the particle positions of the other one. Our investigation utilizes an idea that was exploited previously to provide group-theoretic interpretation for several dualities discovered originally by Ruijsenaars. In the group-theoretic framework, one applies Hamiltonian reduction to two Abelian Poisson algebras of invariants on a higher dimensional phase space and identifies their reductions as action and position variables of two integrable systems living on two different models of the single reduced phase space. Taking the cotangent bundle of U(2n) as the upstairs space, we demonstrate how this mechanism leads to a new dual pair involving the BCn trigonometric Sutherland system. Thereby, we generalize earlier results pertaining to the An trigonometric Sutherland system as well as a recent work by Pusztai on the hyperbolic BCn Sutherland system.

Original languageEnglish
Article number102704
JournalJournal of Mathematical Physics
Volume55
Issue number10
DOIs
Publication statusPublished - Oct 17 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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