论文标题
在最大一能群的作用下，栖息地对称空间的几何形状
Geometry of Hermitian symmetric spaces under the action of a maximal unipotent group
论文作者
论文摘要
令$ \，g/k \，$为不可约合的不可约为的赫尔米利亚对称空间，$ \，r \，$，让$ \，nak \，$是$ \ g $的iwasawa分解。通过polydisc定理，$ \，ak/k \，$可以被视为$ \，r $二维管域holomorphorphorphormorphormorphormorphindy嵌入$ \，g/k $的基础。作为$ \，g/k \的每个$ \，n $ -orbit，$在一个点中与$ \，ak/k $相交，因此在$ \，g/k \，g/k \，$，$和$ \ $ cepies in $ copies in $ cepies in $ \ copies的$ \，g/k/k \，g/k \，$ \，g/k/k/k \，$ \，g/k/k/k/k/k/k/invariant域之间有一对一的对应关系。在这种情况下，我们证明了Bochner的管定理的概括。也就是说，一个$ \，n $ invariant域$ \，d \，d \，in $ \，g/k \，$，$才且仅当基本$ \，ω\，相关管域中的$ $，$，$，convex and cone and``cone and``cone不变式''。 $ \，n $ invariant域，$ \，g/k $。
Let $\,G/K\,$ be a non-compact irreducible Hermitian symmetric space of rank $\,r\,$ and let $\,NAK\,$ be an Iwasawa decomposition of $\,G$. By the polydisc theorem, $\,AK/K\,$ can be regarded as the base of an $\,r$-dimensional tube domain holomorphically embedded in $\,G/K$. As every $\,N$-orbit in $\,G/K\,$ intersects $\,AK/K$ in a single point, there is a one-to-one correspondence between $\,N$-invariant domains in $\,G/K\,$ and tube domains in the product of $\,r\,$ copies of the upper half-plane in $\,\C$. In this setting we prove a generalization of Bochner's tube theorem. Namely, an $\,N$-invariant domain $\,D\,$ in $\,G/K\,$ is Stein if and only if the base $\,Ω\,$ of the associated tube domain is convex and ``cone invariant". We also obtain a precise description of the envelope of holomorphy of an arbitrary holomorphically separable $\,N$-invariant domain over $\,G/K$.
