Trigonometric Real Form of the Spin RS Model of Krichever and Zabrodin

Fairon M.; Feher L.; Marshall I.

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Trigonometric Real Form of the Spin RS Model of Krichever and Zabrodin

机译：Krichever和Zabrodin的旋转RS模型的三角真实形式

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We investigate the trigonometric real form of the spin Ruijsenaars-Schneider system introduced, at the level of equations of motion, by Krichever and Zabrodin in 1995. This pioneering work and all earlier studies of the Hamiltonian interpretation of the system were performed in complex holomorphic settings; understanding the real forms is a nontrivial problem. We explain that the trigonometric real form emerges from Hamiltonian reduction of an obviously integrable `free' system carried by a spin extension of the Heisenberg double of the U(n) Poisson-Lie group. The Poisson structure on the unreduced real phase space GL(n, C) xC(nd) is the direct product of that of the Heisenberg double and d >= 2 copies of a U(n) covariant Poisson structure on C-n similar or equal to R-2n found by Zakrzewski, also in 1995. We reduce by fixing a group valued moment map to a multiple of the identity and analyze the resulting reduced system in detail. In particular, we derive on the reduced phase space the Hamiltonian structure of the trigonometric spin Ruijsenaars-Schneider system and we prove its degenerate integrability.

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《Annales Henri Poincare》 |2021年第2期|共61页
作者
Fairon M.; Feher L.; Marshall I.;
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Univ Glasgow Sch Math &

Stat Univ Pl Glasgow G12 8QQ Lanark Scotland;

Univ Szeged Dept Theoret Phys Tisza Lajos Krt 84-86 H-6720 Szeged Hungary;

Natl Res Univ Fac Math Higher Sch Econ Usacheva 6 Moscow Russia;

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中图分类理论物理学;
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Trigonometric Real Form of the Spin RS Model of Krichever and Zabrodin

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