三角与有理自旋Calogero-Sutherland模型的高阶哈密顿量之间的关系
Relations between the higher Hamiltonians of the trigonometric and the rational spin Calogero-Sutherland models
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中文总结 AI 辅助
本文通过两种嵌套结构建立了三角与有理Dunkl算子生成的哈密顿量层级间的精确与首项重构关系，并用N色杨图和Maya图解释三角模型本征值。
中文摘要 AI 辅助
本文研究了由三角Cherednik-Dunkl算子生成的哈密顿量层级与由有理Dunkl算子生成的哈密顿量层级之间的关系。我们发展了两种嵌套结构来联系这两个层级。第一种嵌套关系从三角自旋Calogero-Sutherland哈密顿量精确重构出高阶有理自旋Calogero-Sutherland哈密顿量。第二种嵌套关系从有理自旋Calogero-Sutherland哈密顿量重构出高阶三角自旋Calogero-Sutherland哈密顿量的首项。此外，我们利用$N$色杨图和Maya图解释了三角自旋Calogero-Sutherland哈密顿量的本征值。
英文摘要
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.
发表机构
- School of Mathematical Sciences, Capital Normal University（首都师范大学数学科学学院）
- Beijing International Center for Mathematical Research（北京国际数学研究中心）
- Beijing Institute of Mathematical Sciences and Applications（北京应用数学与计算科学研究所）
- Mathematical Sciences Center, Tsinghua University（清华大学数学科学中心）
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