双仿射RS对应关系的对偶权重与单值群
Dual Weight and Monodromy of Dual Affine RS Correspondence
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中文总结 AI 辅助
该研究针对扩展仿射置换的两种参数化方式，引入对偶权重β，证明其与AMBC权重ρ在仿射Knuth路径上单值群一致，且二者差值仅取决于关联杨表。
中文摘要 AI 辅助
双仿射Robinson–Schensted对应关系与仿射矩阵球构造（AMBC）为扩展仿射置换提供了两种相关参数化方式。从对偶对应关系的稳定窗口数据出发，我们引入对偶权重β并证明其与原始对(λ,N₀)一致；证明β与AMBC权重ρ在仿射Knuth路径上具有相同单值群，还给出β与ρ的显式关系，表明二者的差值仅取决于关联的杨表。
英文摘要
The dual affine Robinson--Schensted correspondence and the affine matrix-ball construction give two related parametrizations of extended affine permutations. From the stable-window data of the dual correspondence, we introduce a dual weight \(β\) and prove that it is consistent with the original pair \((λ,N_0)\). We prove that \(β\) and the AMBC weight \(ρ\) have identical monodromy along affine Knuth paths. We further give an explicit relation between \(β\) and \(ρ\), showing that their difference depends only on the associated tabloids.
