Pavel Drozdov

Algebraic approach to superintegrability, discrete-time systems, and polynomial algebra deformations: recent developments

In this talk, we focus on the algebraic approach to continuous- and discrete-time superintegrable systems. We review the methodology and discuss some recent results [1, 2]. In particular, we present the complete structure of the symmetry algebras associated with the N-body Calogero-Moser system, the Ruijsenaars-Schneider model, and their maximally superintegrable discretizations. Through these examples, we show how discretization naturally leads to nontrivial deformations of the corresponding continuous symmetry algebras, with the discretization parameter playing the role of a deformation parameter. This phenomenon illustrates how discrete superintegrable systems can be viewed as natural sources of deformed polynomial algebraic structures. 

[1] P. Drozdov, G. Gubbiotti, and D. Latini. Discrete-time maximally superintegrable systems and deformed symmetry algebras: the Calogero-Moser case. In:  Phys. D: Nonlin. Phenom.  496 (2026), p. 135323.

url: doi.org/10.1016/j.physd.2026.135323. arXiv:2601.10625 [math-ph] 

[2] P. Drozdov. Superintegrability of discrete-time rational Ruijsenaars-Schneider model and deformed polynomial symmetry algebras. In preparation (2026).