AI 中文总结
该研究基于归一化黎曼-希尔伯特分解构建ASDYM层次的佐藤理论dressing框架，推导了相关方程与流，通过维数约化恢复经典可积层次，为解决沃德猜想提供了理论基础。
AI 中文摘要
我们基于归一化黎曼-希尔伯特分解，为反自对偶杨-米尔斯（ASDYM）层次构建了佐藤理论的 dressing 框架。生成函数的四扇区展开产生了相对坐标的双无限矩阵阵列，扩展了佐藤格拉斯曼大胞上的仿射坐标。我们推导了佐藤-威尔逊方程、连续坐标流及其离散类似物，在维数约化约束下恢复了若干经典可积层次，其非线性变量被识别为特定相对坐标。
英文摘要
We develop the Sato-theoretic dressing framework for the anti-self-dual Yang-Mills (ASDYM) hierarchy based on a normalized Riemann-Hilbert decomposition. A four-sector expansion of the generating function yields a bi-infinite matrix array of relative coordinates, extending the affine coordinates on the big cell of the Sato Grassmannian. We derive the Sato-Wilson equations, continuous coordinate flows, and their discrete analogues. Several classical integrable hierarchies are recovered under dimensional reduction constraints, with their nonlinear variables identified as specific relative coordinates.
