Correspondence between Calogero-Moser systems and integrable SL(N,$\mathbb{C}$) Euler-Arnold tops

Andrey Smirnov

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arXiv · 0809.2187

Correspondence between Calogero-Moser systems and integrable SL(N,$\mathbb{C}$) Euler-Arnold tops

Andrey Smirnov

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Abstract

The equivalence between the N-particle Calogero-Moser systems and the integrable sl(N,$\mathbb{C}$)-tops is shown. New rational and trigonometric classical Lax operators for these systems are found. Relations with new solutions of the classical Yang-Baxter equations for sl(N,$\mathbb{C}$) are discussed. Explicit formulae for N=2,3,4 are presented.

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Andrey Smirnov. 2008-09-12. Correspondence between Calogero-Moser systems and integrable SL(N,$\mathbb{C}$) Euler-Arnold tops. https://arxiv.org/abs/0809.2187

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