相关论文: Integrable spin Calogero-Moser systems
A family of integrable $GL(NM)$ models is described. On the one hand it generalizes the classical spin Ruijsenaars--Schneider systems (the case $N=1$), and on the other hand it generalizes the relativistic integrable tops on $GL(N)$ Lie…
We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with…
The purpose of this paper is to bring together various loose ends in the theory of integrable systems. For a semisimple Lie algebra $\mathfrak g$, we obtain several results on completeness of homogeneous Poisson-commutative subalgebras of…
After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson…
A two-dimensional integrable system being a deformation of the rational Calogero-Moser system is constructed via the symplectic reduction, performed with respect to the Sklyanin algebra action. We explicitly resolve the respective classical…
We provide some details about the recently discovered integrable systems implied by commutativity of $W$ operators along the rays on the plane of roots of $w_\infty$-algebra. The simplest system of this type is the rational Calogero model,…
The Lax pair for the field analogue of the classical spin elliptic Calogero-Moser is proposed. Namely, using the previously known Lax matrix we suggest an ansatz for the accompany matrix. The presented construction is valid when the matrix…
We construct twisted Calogero-Moser (CM) systems with spins as the Hitchin systems derived from the Higgs bundles over elliptic curves, where transitions operators are defined by an arbitrary finite order automorphisms of the underlying Lie…
The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero-Moser systems. In the special case of symmetric pair g=gl(n,2m),…
We show how the elliptic Calogero-Moser integrable systems arise from a symplectic quotient construction, generalising the construction for A_{N-1} by Gorsky and Nekrasov to other algebras. This clarifies the role of (twisted) affine…
Integrable spin Calogero-Moser type systems with non-symmetric configurations of the singularities of the potential appeared in the work of Chalykh, Goncharenko, and Veselov in 1999. We obtain various generalisations of these examples by…
This paper presents a comprehensive description of the coordinate rings and Poisson brackets associated with the fourth Calogero-Moser space and invariant commuting pairs of matrices of size four. As an application, we compute their…
The universal formulation of spin exchange models related to Calogero-Moser models implies the existence of integrable hierarchies, which have not been explored. We show the general structures and features of the spin exchange model…
In recent years methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this note it is shown that the latter method is actually…
Recent results are surveyed pertaining to the complete integrability of some novel n-particle models in dimension one. These models generalize the Calogero-Moser systems related to classical root systems. Quantization leads to difference…
We consider three 'classical doubles' of any semisimple, connected and simply connected compact Lie group $G$: the cotangent bundle, the Heisenberg double and the internally fused quasi-Poisson double. On each double we identify a pair of…
We completely classify the real root subsystems of root systems of loop algebras of Kac-Moody Lie algebras. This classification involves new notions of "admissible subgroups" of the coweight lattice of a root system $\Psi$, and "scaling…
We present an elementary discussion of the Calogero-Moser model. This gives us an opportunity to illustrate basic concepts of the dynamical integrable models. Some ideas are also presented regarding interconnections between integrable…
We present a general framework for constructing polynomial integrable systems on linearizations of Poisson varieties that admit log-canonical systems. Our construction is in particular applicable to Poisson varieties with compatible cluster…
We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are…