Related papers: Generalised Calogero-Moser models and universal La…
We present a derivation of the dynamical r-matrices of the Calogero-Moser models using the Hamiltonian reduction procedure to get general formulae. We describe the dynamical r-matrices thus found for spin Calogero-Moser models and…
The Calogero model is an interacting, $N$-particle, $\mathfrak{sl}(2,\mathbb R)$-invariant quantum mechanics, whose Hilbert space is furnished by a tower of discrete series modules. The system enjoys both classical and quantum integrability…
We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system as a particular case. For the general class, we introduce separation…
Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and…
We discuss a special eigenstate of the quantized periodic Calogero-Moser system associated to a root system. This state has the property that its eigenfunctions, when regarded as multivalued functions on the space of regular conjugacy…
Liouville integrability of classical Calogero-Moser models is proved for models based on any root systems, including the non-crystallographic ones. It applies to all types of elliptic potentials, i.e. untwisted and twisted together with…
Explicit algebraic relations between the quantum integrals of the elliptic Calogero--Moser quantum problems related to the root systems ${\bf A_2}$ and ${\bf B_2}$ are found.
The equations that define the Lax pairs for generalized principal chiral models can be solved for any nondegenerate bilinear form on $su(2)$. The solution is dependent on one free variable that can serve as the spectral parameter.
Field equations for generalized principle models with nonconstant metric are derived and ansatz for their Lax pairs is given. Equations that define the Lax pairs are solved for the simplest solvable group. The solution is dependent on one…
The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a…
Explicit algebraic relations between the quantum integrals of the elliptic Calogero-Moser quantum problems related to the root systems A_2 and B_2 are found.
We construct integrable generalizations of the elliptic Calogero-Sutherland-Moser model of particles with spin, involving noncommutative spin interactions. The spin coupling potential is a modular function and, generically, breaks the…
We construct the $r$-matrix for the generalization of the Calogero-Moser system introduced by Gibbons and Hermsen. By reduction procedures we obtain the $r$-matrix for the $O(N)$ Euler-Calogero-Moser model and for the standard $A_N$…
There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the…
In this paper, we construct a new Lax operator for the elliptic $A_{n-1}$ Calogero-Moser model with general $n(2\leq n$) from the classical dynamical twisting,in which the corresponding r-matrix is purely numeric (nondynamical one). The…
Lax operator algebras for the root system $G_2$, and arbitrary finite genus Riemann surfaces and Tyurin data on them are constructed.
We present a worked example for the new extensions of the multi-particle Calogero model endowed with infinite Weyl group symmetry of affine and hyperbolic type. Building upon the hyperbolic extension of the $A_3$-Kac-Moody algebra, we…
New classical integrable systems of Camassa-Holm peakon type are proposed. They realize the maximal even piecewise-D_2 generalization of the Calogero-Francoise flows, yielding periodic and pseudoperiodic trigonometric/hyperbolic potentials.…
The notion of $\mathcal{O}$-operators on modules over Lie algebras generalize Rota-Baxter operators. They also generalize Poisson structures on Lie algebras in the presence of modules. Motivated from Poisson structures, we define gauge…
A special class of solutions to the generalised WDVV equations related to a finite set of covectors is investigated. Some geometric conditions on such a set which guarantee that the corresponding function satisfies WDVV equations are found…