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PreprintCC BY-NC-ND 4.0arXiv

Symmetries of the Generalized Yang--Baxter Equations

  • Pramod Padmanabhan
  • Somnath Maity
  • Akash Sinha
  • Vladimir Korepin
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Abstract

The generalized Yang-Baxter equations are multi-site versions of the standard Yang-Baxter equation. When spectral parameters are included, such equations are expected to lead to integrable Hamiltonians with local interactions involving multiple degrees of freedom. In this work we characterize both the continuous and discrete symmetries of these equations required to establish an equivalence class of solutions. We find that the set of such symmetries depends on the number of sites on which the equation is supported. In several cases there are more symmetries than the standard Yang-Baxter equation, thus placing heavy constraints on the number of inequivalent solutions and the associated integrable models. As an application we show how to restrict the generic 16×16 ansatz to the 30-dimensional subspace invariant under a chosen discrete symmetry subgroup. An explicit 16× 16 solution is also written down.

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Cite

BibTeXRIS
BibTeX
@misc{padmanabhan2026symmetries,
  title = {{Symmetries of the Generalized Yang--Baxter Equations}},
  author = {Pramod Padmanabhan and Somnath Maity and Akash Sinha and Vladimir Korepin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.26510},
  eprint = {2606.26510},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.26510},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Symmetries of the Generalized Yang--Baxter Equations
AU  - Pramod Padmanabhan
AU  - Somnath Maity
AU  - Akash Sinha
AU  - Vladimir Korepin
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2606.26510
UR  - https://arxiv.org/abs/2606.26510
AB  - The generalized Yang-Baxter equations are multi-site versions of the standard Yang-Baxter equation. When spectral parameters are included, such equations are expected to lead to integrable Hamiltonians with local interactions involving multiple degrees of freedom. In this work we characterize both the continuous and discrete symmetries of these equations required to establish an equivalence class of solutions. We find that the set of such symmetries depends on the number of sites on which the equation is supported. In several cases there are more symmetries than the standard Yang-Baxter equation, thus placing heavy constraints on the number of inequivalent solutions and the associated integrable models. As an application we show how to restrict the generic 16×16 ansatz to the 30-dimensional subspace invariant under a chosen discrete symmetry subgroup. An explicit 16× 16 solution is also written down.
ER  -