发表机构
Beijing Institute for Mathematical Sciences and Applications（北京数学与应用数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用q-算子的代数几何语言，建立了B/C/D型经典哈密顿量能级集与带开边界条件的A型XXZ Bethe Ansatz方程解集的双射，推广了经典对偶结果，还引入了ℤ/2ℤ折叠与非简约BC型系统。
AI 中文摘要
本文利用q-算子（q-opers）的语言，对量子XXZ自旋链的Bethe Ansatz方程与经典群的多体三角Ruijsenaars-Schneider/Macdonald系统之间的对偶关系给出了代数几何描述。在此对偶下，B/C/D型经典哈密顿量的能级集与A型XXZ Bethe Ansatz方程（带开边界条件）的解集存在双射，该结论推广了此前GL(N) XXZ自旋链（带扭曲周期边界条件）与N体Ruijsenaars-Schneider系统对偶的结果。我们的构造在(GL(N),q)-算子数据和N体三角Ruijsenaars-Schneider模型层面均实现了ℤ/2ℤ折叠，分析中还出现了非简约BC型系统。
英文摘要
Using the language of q-opers, we propose an algebro-geometric description of the duality between Bethe Ansatz equations for quantum XXZ spin chains and many-body trigonometric Ruijsenaars-Schneider/Macdonald systems for classical groups. Upon this duality, the energy level sets of the classical B/C/D-type Hamiltonians are found to be in bijection with the set of solutions of the XXZ Bethe Ansatz equations of type A, albeit with open boundary conditions. This dictionary generalizes previous results in which a GL(N) XXZ spin chain with twisted periodic boundary conditions was dual to an N-body Ruijsenaars-Schneider system. Our construction implements a $\mathbb{Z}/2\mathbb{Z}$ folding both at the level of the (GL(N),q)-oper data as well as at the level of the N-body trigonometric Ruijsenaars-Schneider model. The nonreduced BC-type systems appear in our analysis as well.
Comments60 pages, references added, minor corrections
