Generalized Calogero-Moser-Sutherland models from geodesic motion on GL(n, R) group manifold
Abstract
It is shown that geodesic motion on the GL(n, R) group manifold endowed with the bi-invariant metric d s^2 = tr(g^{-1} d g)^2 corresponds to a generalization of the hyperbolic n-particle Calogero-Moser-Sutherland model. In particular, considering the motion on Principal orbit stratum of the SO(n, R) group action, we arrive at dynamics of a generalized n-particle Calogero-Moser-Sutherland system with two types of internal degrees of freedom obeying SO(n, R) \bigoplus SO(n, R) algebra. For the Singular orbit strata of SO(n, R) group action the geodesic motion corresponds to certain deformations of the Calogero-Moser-Sutherland model in a sense of description of particles with different masses. The mass ratios depend on the type of Singular orbit stratum and are determined by its degeneracy. Using reduction due to discrete and continuous symmetries of the system a relation to II A_n Euler-Calogero-Moser-Sutherland model is demonstrated.
Keywords
Cite
@article{arxiv.nlin/0103047,
title = {Generalized Calogero-Moser-Sutherland models from geodesic motion on GL(n, R) group manifold},
author = {A. M. Khvedelidze and D. M. Mladenov},
journal= {arXiv preprint arXiv:nlin/0103047},
year = {2009}
}
Comments
16 pages, LaTeX, no figures. V2: Typos corrected, two references added. V3: Abstract changed, typos corrected, a few formulas and references added. The presentation in the last section has been clarified and it was restricted to the case of GL(3, R) group, the analysis of GL(4, R) will be given elsewhere. V4: Minor corrections in the whole text, more formulas and references added, accepted for publication in PLA