到酉群实形式的调和映射

On Harmonic Maps into a Real Form of Unitary Group U(N)

研究从单连通区域Ω R2 ∪ {∞ }到酉群U(N)的某一类实形式G(包括正交群和辛群 )的调和映射 ,引入了G uniton和扩张G uniton的概念 ,并通过两次dressing作用和奇异Darboux变换给出了G uniton及其旗因子的纯代数构造方法 .证明了任意具有有限uniton数的调和映射 φ :Ω →G可因子分解为有限个G

The harmonic maps from a simply connected domain ΩR 2∪{∞} into some real forms of unitary group U(N),which contain symplectic groups and orthogonal groups,are studied.The G uniton and extended G uniton are introduced.The method of the dressing action and the singular Darboux transformation is used to construct G uniton and G flag factor.It is proved that any harmonic map φ:Ω→G with finite uniton number can be factorized into a product of a finite number of G unitons.