2026/01/15 by Pavel Drozdov, Giorgio Gubbiotti, Danilo Latini
Physics and Astronomy · Mathematics · #Quantum Mechanics and Non-Hermitian Physics #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons
paper · pdf · doi:10.1016/j.physd.2026.135323
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 continuous symmetry algebra, with the discretization parameter playing the rôle of a deformation parameter. This phenomenon illustrates how discrete superintegrable systems can be viewed as natural sources of deformed polynomial algebraic structures. As a byproduct of these results, we also reveal a connection between the above-mentioned symmetry algebras and the Bell polynomials, as a consequence of the trace properties.