Related papers: Quantum integrability of the deformed elliptic Cal…
We consider ideals of polynomials vanishing on the W-orbits of the intersections of mirrors of a finite reflection group W. We determine all such ideals which are invariant under the action of the corresponding rational Cherednik algebra…
We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the…
We study the integrability and the Bethe/Gauge correspondence of the Generalized Calogero-Moser system proposed by Berntson, Langmann and Lenells which we call the elliptic quadruple Calogero-Moser system (eqCM). We write down the Dunkl…
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 propose the integrable N-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems and construct their constants of motion via the Dunkl operators. Their Schr\"odinger equations decouple in parabolic and elliptic…
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…
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…
We consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlev\'e equation. We establish an extended symmetry, complementing known results. The Calogero-Moser…
This review article discusses recent progress in understanding of various families of integrable models in terms of algebraic geometry, representation theory, and physics. In particular, we address the connections between soluble many-body…
Searching for integrable models is a central theme in theoretical and mathematical physics, as such systems offer valuable insights into the underlying structure and symmetries of complex physical phenomena. In this work, we contribute to…
We analyse the $n$-dimensional superintegrable Kepler-Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure…
We determine the complete structure of the symmetry algebras associated with the N-body Calogero-Moser system and its maximally superintegrable discretization. We prove that the discretization naturally leads to a nontrivial deformation of…
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 that elliptic Calogero-Moser system and its Lax operator found by Krichever can be obtained by Hamiltonian reduction from the integrable Hamiltonian system on the cotangent bundle to the central extension of the algebra of SL(N,C)…
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…
Explicit solutions for one completely-integrable system of Calogero-Moser type in external fields are found in case of three and four interacting particles. Relation between coupling constant, initial values of coordinates and time of…
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…
In this review we explain interrelations between the Elliptic Calogero-Moser model, integrable Elliptic Euler-Arnold top, monodromy preserving equations and the Knizhnik-Zamolodchikov-Bernard equation on a torus.
We show that the integrability of the dynamical system recently proposed by Calogero and characterized by the Hamiltonian $ H = \sum_{j,k}^{N} p_j p_k \{\lambda + \mu cos [ \nu ( q_j - q_k)] \} $ is due to a simple algebraic structure . It…
This paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of gl(N). Various results about these subalgebras are proven by presenting them in the notation of…