Trigonometric Sutherland systems and their Ruijsenaars duals from symplectic reduction
- Department of Theoretical Physics, MTA KFKI RMKI, P.O. Box 49, H-1525 Budapest (Hungary)
- Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, H-6720 Szeged (Hungary)
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)xSU(n) and RxSU(n), respectively. This geometric interpretation enhances our understanding of the duality relations and simplifies Ruijsenaars' original direct arguments that led to their discovery.
- OSTI ID:
- 21476583
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 10; Other Information: DOI: 10.1063/1.3492919; (c) 2010 American Institute of Physics; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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