Spin Calogero-Moser models on symmetric spaces

2019/03/08 by N. Reshetikhin, Reshetikhin, N.
Mathematics · Physics and Astronomy · #37J40 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1903.03685

openalex publication_date 2019/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct and prove superintegrability of spin Calogero-Moser type systems on symplectic leaves of K₁\backslash T^*G/K₂ where K₁,K₂⊂ G are subgroups. We call them two sided spin Calogero-Moser systems. One important type of such systems correspond to K₁=K₂=K where K is a subgroup of fixed points of Chevalley involution θ: G→ G. The other important series of examples come from pair G⊂ G× G with the diagonal embedding. We explicitly describe examples of such systems corresponding to symplectic leaves of rank one when G=SL_n.

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