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PreprintarXiv licencearXiv

Relations between the higher Hamiltonians of the trigonometric and the rational spin Calogero-Sutherland models

  • Yue Li
  • Fan Liu
  • Lu-Yao Wang
  • Jie Yang
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Abstract

In this paper we study the relations between the Hamiltonian hierarchy generated by trigonometric Cherednik-Dunkl operators and the one generated by rational Dunkl operators. We develop two nested structures relating these two hierarchies. The first nested relation reconstructs the higher rational spin Calogero-Sutherland Hamiltonians exactly from the trigonometric ones. The second nested relation reconstructs the higher trigonometric spin Calogero-Sutherland Hamiltonians as leading terms from the rational ones. In addition, we provide an explanation of the eigenvalues of the trigonometric spin Calogero-Sutherland Hamiltonians in terms of N-colored Young diagrams and Maya diagrams.

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Cite

BibTeXRIS
BibTeX
@misc{li2026relations,
  title = {{Relations between the higher Hamiltonians of the trigonometric and the rational spin Calogero-Sutherland models}},
  author = {Yue Li and Fan Liu and Lu-Yao Wang and Jie Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14330},
  eprint = {2609.14330},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14330},
}
RIS
TY  - UNPB
TI  - Relations between the higher Hamiltonians of the trigonometric and the rational spin Calogero-Sutherland models
AU  - Yue Li
AU  - Fan Liu
AU  - Lu-Yao Wang
AU  - Jie Yang
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14330
UR  - https://arxiv.org/abs/2609.14330
AB  - In this paper we study the relations between the Hamiltonian hierarchy generated by trigonometric Cherednik-Dunkl operators and the one generated by rational Dunkl operators. We develop two nested structures relating these two hierarchies. The first nested relation reconstructs the higher rational spin Calogero-Sutherland Hamiltonians exactly from the trigonometric ones. The second nested relation reconstructs the higher trigonometric spin Calogero-Sutherland Hamiltonians as leading terms from the rational ones. In addition, we provide an explanation of the eigenvalues of the trigonometric spin Calogero-Sutherland Hamiltonians in terms of N-colored Young diagrams and Maya diagrams.
ER  -