在调和映射空间上的Dressing作用

Dressing Action on Space of Harmonic Maps

得到Dressing作用的一些性质 ,证明标准的n uniton扩张解在Dressing作用下仍然是标准的n uniton扩张解 ,因而Dressing作用保持有限调和映射的极小uniton数不变 (后面的结论已被Guest和Ohnita证明 ) .特别证明对于全纯映射 ,Dressing作用仅与群元素在零点值有关 .此性质表明Loop群在全纯映射上的作用与复线性群在复Grassman nians上的标准作用是等价的 .

It is proved that standard extended solution with n uniton will be transformed into standard extended solution with n uniton under dressing action.It follows that dressing action preserves minimal uniton number.It is also proved that loop group action on holomorphic maps is equivalent to complex linear group action on Grassmannians.