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Superintegrability of discrete-time rational Ruijsenaars-Schneider model and deformed polynomial symmetry algebras

  • Pavel Drozdov
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Abstract

We explicitly construct the additional integrals of motion, ensuring maximal superintegrability of the discrete-time rational Ruijsenaars-Schneider model. Using them, we investigate the algebraic aspects of superintegrability in both continuous- and discrete-time settings. In particular, we determine the complete structures of the polynomial symmetry algebras associated with both the rational Ruijsenaars-Schneider model and its discretization. We demonstrate that discretization leads to a nontrivial deformation of the continuous symmetry algebra with respect to the discretization parameter, thereby extending recent analogous results from the rational Calogero-Moser system to its relativistic generalization.

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Cite

BibTeXRIS
BibTeX
@misc{drozdov2026superintegrability,
  title = {{Superintegrability of discrete-time rational Ruijsenaars-Schneider model and deformed polynomial symmetry algebras}},
  author = {Pavel Drozdov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.30065},
  eprint = {2609.30065},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30065},
}
RIS
TY  - UNPB
TI  - Superintegrability of discrete-time rational Ruijsenaars-Schneider model and deformed polynomial symmetry algebras
AU  - Pavel Drozdov
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.30065
UR  - https://arxiv.org/abs/2609.30065
AB  - We explicitly construct the additional integrals of motion, ensuring maximal superintegrability of the discrete-time rational Ruijsenaars-Schneider model. Using them, we investigate the algebraic aspects of superintegrability in both continuous- and discrete-time settings. In particular, we determine the complete structures of the polynomial symmetry algebras associated with both the rational Ruijsenaars-Schneider model and its discretization. We demonstrate that discretization leads to a nontrivial deformation of the continuous symmetry algebra with respect to the discretization parameter, thereby extending recent analogous results from the rational Calogero-Moser system to its relativistic generalization.
ER  -