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On a Poisson-Lie deformation of the BCn Sutherland system

Fehér, László Gyula and Görbe, Tamás Ferenc (2015) On a Poisson-Lie deformation of the BCn Sutherland system. NUCLEAR PHYSICS B, 901. pp. 85-114. ISSN 0550-3213

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Abstract

A deformation of the classical trigonometric BCn 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 BCn Sutherland system. We prove that this yields a Liouville integrable Hamiltonian system and construct a globally valid model of the smooth re- duced phase space wherein the commuting flows are complete. We point out that the reduced system, which contains 3 independent coupling constants besides the deforma- tion 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).

Item Type: Article
Subjects: Q Science / természettudomány > QC Physics / fizika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 23 Nov 2023 15:10
Last Modified: 23 Nov 2023 15:10
URI: http://real.mtak.hu/id/eprint/180777

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