Spin Calogero-Moser systems associated with simple Lie algebras

Integrable spin Calogero-Moser systems

We introduce spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. The associated integrable models (called integrable spin Calogero-Moser systems in the paper) and their Lax pairs are then obtained via Poisson reduction and gauge transformations. For Lie algebras of $A_{n}$-type, this new class of integrable systems includes the usual Calogero-Moser systems as subsystems. Our method is guided by a general framework which we develop here using dynamical Lie…

Degenerate Integrability of Spin Calogero-Moser Systems and the duality with the spin Ruijsenaars systems

It is shown that spin Calogero-Moser systems are completely integrable in a sense of degenerate integrability. Their Liouville tori have dimension less then half of the dimension of the phase space. It is also shown that rational spin Ruijsenaars systems are degenerately integrable and dual to spin Calogero- Moser systems in a sense that action-algle variables of one are angle-action variables of the other.

Periodic and open classical spin Calogero-Moser chains

We construct a class of interacting spin Calogero-Moser type systems. They can be regarded as a many particle system with spin degrees of freedom and as an integrable spin chain of Gaudin type. We prove that these Hamiltonian systems are superintegrable.

Singular cotangent bundle reduction and spin Calogero-Moser systems

We develop a bundle picture for the case that the configuration manifold has only a single isotropy type, and give a formula for the reduced symplectic form in this setting. Furthermore, as an application of this bundle picture we consider Calogero-Moser systems with spin associated to polar representations of compact Lie groups.

Calogero-Moser空间的辛全纯密度性质

The symplectic holomorphic density property for Calogero-Moser spaces

本文引入辛全纯密度性质等概念及对应理论，证明n粒子Calogero-Moser空间$\mathcal{C}_n$具有该性质并刻画其全纯辛自同构群，为相关空间的自同构研究提供基础。

Spin Calogero-Moser models on symmetric spaces

In this paper we construct and prove superintegrability of spin Calogero-Moser type systems on symplectic leaves of $K_1\backslash T^*G/K_2$ where $K_1,K_2\subset G$ are subgroups. We call them two sided spin Calogero-Moser systems. One important type of such systems correspond to $K_1=K_2=K$ where $K$ is a subgroup of fixed points of Chevalley involution $θ: G\to G$. The other important series of examples come from pair $G\subset G\times G$ with the diagonal embedding. We explicitly describe examples of such systems corresponding to symplectic leaves of rank one when $G=SL_n$.