AI 中文总结
研究受$A$型DAHA启发的$N$体Cherednik可积系统，通过类似Noumi和Shiraishi的方法，构造任意特征值的本征函数，其一般本征函数结构复杂，有$N!$个分支，还给出特定情形显式公式。
AI 中文摘要
$n$变量的对称Macdonald多项式为$N$体三角Ruijsenaars-Schneider可积系统在特定特征值处提供本征函数。为构造任意特征值的本征函数，M. Noumi和J. Shiraishi对对称Macdonald多项式使用了$N$中的递归（分支规则）并进行解析延拓，生成了一个幂级数，它是三元组（通用解）的一部分。本文表明，类似过程可用于另一个可积系统，即受$A$型DAHA启发的$N$体Cherednik系统，其多项式本征函数为非对称Macdonald多项式。但在该系统中，一般本征函数更复杂：它不像Noumi-Shiraishi情形那样只是简单幂级数，而是具有包含$N!$个分支的复杂结构，每个分支都是Noumi-Shiraishi型的幂级数。作为示例，我们还给出了特定情形的显式公式。
英文摘要
Symmetric Macdonald polynomials of $N$ variables provide eigenfunctions of the $N$-body trigonometric Ruijsenaars-Schneider integrable system at particular eigenvalues. In order to construct eigenfunctions with arbitrary eigenvalues, M. Noumi and J. Shiraishi used a recursion in $N$ (branching rule) for the symmetric Macdonald polynomials and analytically continued them. This generated a power series, which is a part of triad (universal solution). In the present paper, we demonstrate that a similar procedure is available for another integrable system, $N$-body Cherednik integrable system inspired by the DAHA of type $A$, which has non-symmetric Macdonald polynomials as its polynomial eigenfunctions. However, in this system, the generic eigenfunction is more complicated: it is not just a simple power series as in the Noumi-Shiraishi case, but has an involved structure with $N!$ branches, each of them being a sum over the Weyl chambers of power series of the Noumi-Shiraishi type. As an illustration, we also provide explicit formulas for particular cases.
Comments14+8 pages
Journal refPhys.Lett. B881 (2026) 140902
DOI：10.1016/j.physletb.2026.140902
