Trigonometric Sutherland systems and their Ruijsenaars duals from symplectic reduction

L. Fehér, V. Ayadi

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11 Citations (Scopus)

Abstract

Beside its usual interpretation as a system of n indistinguishable particles moving on the circle, the trigonometric Sutherland system can be viewed alternatively as a system of distinguishable particles on the circle or on the line, and these three physically distinct systems are in duality with corresponding variants of the rational Ruijsenaars-Schneider system. We explain that the three duality relations, first obtained by Ruijsenaars in 1995, arise naturally from the Kazhdan-Kostant-Sternberg symplectic reductions of the cotangent bundles of the group U(n) and its covering groups U(1)×SU(n) and R×SU(n), respectively. This geometric interpretation enhances our understanding of the duality relations and simplifies Ruijsenaars' original direct arguments that led to their discovery.

Original languageEnglish
Article number103511
JournalJournal of Mathematical Physics
Volume51
Issue number10
DOIs
Publication statusPublished - Oct 1 2010

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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