Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-07-18
J.Phys. A37 (2004) 11841-11876
Physics
High Energy Physics
High Energy Physics - Theory
45 pages. A few typos in section 6 are corrected
Scientific paper
10.1088/0305-4470/37/49/006
The Ruijsenaars-Schneider systems are `discrete' version of the Calogero-Moser (C-M) systems in the sense that the momentum operator p appears in the Hamiltonians as a polynomial in e^{\pm\beta' p} (\beta' is a deformation parameter) instead of an ordinary polynomial in p in the hierarchies of C-M systems. We determine the polynomials describing the equilibrium positions of the rational and trigonometric Ruijsenaars-Schneider systems based on classical root systems. These are deformation of the classical orthogonal polynomials, the Hermite, Laguerre and Jacobi polynomials which describe the equilibrium positions of the corresponding Calogero and Sutherland systems. The orthogonality of the original polynomials is inherited by the deformed ones which satisfy three-term recurrence and certain functional equations. The latter reduce to the celebrated second order differential equations satisfied by the classical orthogonal polynomials.
Odake Satoru
Sasaki Rei
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