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}
}
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… 

References

SHOWING 1-10 OF 26 REFERENCES
Symplectic duality of symmetric spaces
Hermitian symmetric spaces and Kahler rigidity
AbstractWe characterize irreducible Hermitian symmetric spaces which are not of tube type, both in terms of the topology of the space of triples of pairwise transverse points in the Shilov boundary,
Correction to: “The intersection of two real forms in Hermitian symmetric spaces of compact type”
This talk is based on my joint work with Hiroyuki Tasaki. A real form in a Hermitian symmetric space M of compact type is the fixed point set of an involutive anti-holomorphic isometry of M , which
The diastatic exponential of a symmetric space
AbstractLet (M, g) be a real analytic Kähler manifold. We say that a smooth map Expp : W → M from a neighbourhood W of the origin of TpM into M is a diastatic exponential at p if it satisfies
The Involutions of Compact Symmetric Spaces, IV
In this part, we will construct certain fibrations intended for study of differential geometry, especially that of Riemannian submersions. Their base manifolds are polars and the fibres are
MOMENT MAPS AND ISOPARAMETRIC HYPERSURFACES IN SPHERES — HERMITIAN CASES
We study a relationship between isoparametric hypersurfaces in spheres with four distinct principal curvatures and the moment maps of certain Hamiltonian actions. In this paper, we consider the
The symplectic structure of Kähler manifolds of nonpositive curvature
On montre que la forme de Kahler sur une variete de Kahler complete simplement connexe W de courbure non positive est diffeomorphe a la forme symplectique standard sur R n . Ceci signifie que la
Function Spaces
Linear Algebra in Infinite Dimensions The motivation for our review of linear algebra was the observation that the set of solutions to Schrödinger’s equation satisfies some of the basic requirements
Submanifolds and Holonomy
Basics of Submanifold Theory in Space Forms The fundamental equations for submanifolds of space forms Models of space forms Principal curvatures Totally geodesic submanifolds of space forms Reduction
On special submanifolds in symplectic geometry
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