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arXiv · 2609.14330

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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Yue Li, Fan Liu, Lu-Yao Wang, Jie Yang. 2026-09-13. Relations between the higher Hamiltonians of the trigonometric and the rational spin Calogero-Sutherland models. https://arxiv.org/abs/2609.14330

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