On a Poisson–Lie deformation of the BCn Sutherland system
| Autor: | L. Fehér, T.F. Görbe |
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| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Nuclear Physics B, Vol 901, Iss C, Pp 85-114 (2015) |
| Druh dokumentu: | article |
| ISSN: | 0550-3213 1873-1562 |
| DOI: | 10.1016/j.nuclphysb.2015.10.008 |
| Popis: | 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 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). |
| Databáze: | Directory of Open Access Journals |
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