标题： Poisson-Lie 旋转向量模型的类似物的重新审视 显示英文标题

标题： Poisson-Lie analogues of spin Sutherland models revisited

摘要： 一些自旋Sutherland模型的推广来源于位于紧致半单李群的Heisenberg双上的“主可积系统”。 主系统代表了在相应余切丛上建模的自由运动系统的Poisson-Lie对偶，其约化依赖于对紧致李群的适当共轭作用取商。 我们提供了对约化的增强阐述，并首次严格证明约化系统在对应于相关群作用主轨道类型的Poisson商空间的稠密开子集上具有退化可积性。 在限制到更小的稠密开子集后，也展示了在一般辛叶层上的退化可积性。 本文还包含对约化Poisson结构的新描述，以及对缩放极限的仔细阐述，我们的约化系统在该极限下转化为自旋Sutherland模型。 显示英文摘要

摘要： Some generalizations of spin Sutherland models descend from `master integrable systems' living on Heisenberg doubles of compact semisimple Lie groups. The master systems represent Poisson--Lie counterparts of the systems of free motion modeled on the respective cotangent bundles and their reduction relies on taking quotient with respect to a suitable conjugation action of the compact Lie group. We present an enhanced exposition of the reductions and prove rigorously for the first time that the reduced systems possess the property of degenerate integrability on the dense open subset of the Poisson quotient space corresponding to the principal orbit type for the pertinent group action. After restriction to a smaller dense open subset, degenerate integrability on the generic symplectic leaves is demonstrated as well. The paper also contains a novel description of the reduced Poisson structure and a careful elaboration of the scaling limit whereby our reduced systems turn into the spin Sutherland models.