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).

31 pages. v3: small corrections listed at the beginning of the source file, results unaltered

References in corpus (3)

• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models
• Equivalence of two sets of Hamiltonians associated with the rational BC(n) Ruijsenaars-Schneider-van Diejen system

Cited by in corpus (4)

• The action-angle dual of an integrable Hamiltonian system of Ruijsenaars--Schneider--van Diejen type
• The full phase space of a model in the Calogero-Ruijsenaars family
• Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric ${\mathrm{BC}}_n$ Sutherland system
• Integrable many-body systems of Calogero-Ruijsenaars type