论文标题
非政策类型的Hermitian对称空间的模棱两可的实现
Equivariant realizations of Hermitian symmetric space of noncompact type
论文作者
论文摘要
令$ m = g/k $为非竞争类型的Hermitian对称空间。我们提供了一种构建$ k $ equivariant的嵌入方式，从$ m $到其切好的空间$ t_om $ t_om $ y通过使用$ k $ - action的极性。作为一个应用程序，我们重建了所谓的Harish-Chandra实现的$ K $ Equivariant holomorthric嵌入，以及由DI Scala-Loi和Roos在适当的空间识别下构建的$ K $ Equivariant Symplymorthism。此外，我们通过$ k $ Action的极性来表征$ m $的全态/符号嵌入。此外，我们在$ m $中显示了一类完全大地测量的submanifolds，将$ k $ equivariant嵌入的线性子空间或线性子空间的线性子空间或有限的域。我们还构建了一个$ k $ equivariant的全体形态/符号嵌入，将紧凑型双$ m^*$的开放密集子集构建为$ m $的全态/符号嵌入的双重嵌入。
Let $M=G/K$ be a Hermitian symmetric space of noncompact type. We provide a way of constructing $K$-equivariant embeddings from $M$ to its tangent space $T_oM$ at the origin by using the polarity of the $K$-action. As an application, we reconstruct the $K$-equivariant holomorphic embedding so called the Harish-Chandra realization and the $K$-equivariant symplectomorphism constructed by Di Scala-Loi and Roos under appropriate identifications of spaces. Moreover, we characterize the holomorphic/symplectic embedding of $M$ by means of the polarity of the $K$-action. Furthermore, we show a special class of totally geodesic submanifolds in $M$ is realized as either linear subspaces or bounded domains of linear subspaces in $T_oM$ by the $K$-equivariant embeddings. We also construct a $K$-equivariant holomorphic/symplectic embedding of an open dense subset of the compact dual $M^*$ into its tangent space at the origin as a dual of the holomorphic/symplectic embedding of $M$.
