• DOI:10.1007/s00209-021-02872-x
• Corpus ID: 228063746

Equivariant realizations of Hermitian symmetric space of noncompact type

@article{Hashinaga2021EquivariantRO,
  title={Equivariant realizations of Hermitian symmetric space of noncompact type},
  author={Takahiro Hashinaga and Toru Kajigaya},
  journal={Mathematische Zeitschrift},
  year={2021}
}

• Takahiro Hashinaga, T. Kajigaya
• Published 9 December 2020
• Mathematics
• Mathematische Zeitschrift

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 $M$.