On a Poisson-Lie deformation of the BC(n) Sutherland system
Abstract
A deformation of the classical trigonometric BC(n) Sutherland system is derived via Hamiltonian reduction of the Heisenberg double of SU(2n). We apply a natural Poisson-Lie analogue of the Kazhdan-Kostant-Sternberg type reduction of the free particle on SU(2n) that leads to the BC(n) Sutherland system. We prove that this yields a Liouville integrable Hamiltonian system and construct a globally valid model of the smooth reduced phase space wherein the commuting flows are complete. We point out that the reduced system, which contains 3 independent coupling constants besides the deformation parameter, can be recovered (at least on a dense submanifold) as a singular limit of the standard 5-coupling deformation due to van Diejen. Our findings complement and further develop those obtained recently by Marshall on the hyperbolic case by reduction of the Heisenberg double of SU(n,n).
Keywords
Cite
@article{arxiv.1508.04991,
title = {On a Poisson-Lie deformation of the BC(n) Sutherland system},
author = {L. Feher and T. F. Gorbe},
journal= {arXiv preprint arXiv:1508.04991},
year = {2019}
}
Comments
31 pages. v3: small corrections listed at the beginning of the source file, results unaltered