Visible actions on symmetric spaces
By Toshiyuki Kobayashi. 2006
50 citations recorded by the source corpus.
AbstractA visible action on a complex manifold is a holomorphic action that admits a J-transversal totally real submanifold S. It is said to be strongly visible if there exists an orbit-preserving anti-holomorphic diffeomorphism σ such that σ|S = id. In this paper we prove that for any Hermitian symmetric space D = G/K the action of any symmetric subgroup H is strongly visible. The proof is carried out by finding explicitly an orbit-preserving anti-holomorphic involution and a totally real submanifold S. Our geometric results provide a uniform proof of various multiplicity-free theorems of irreducible highest weight modules when restricted to reductive symmetric pairs, for both classical and exceptional cases, for both finite- and infinite-dimensional cases, and for both discrete and continuous spectra.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1bb8435cc6102d3f8031356b6fb47346d9e5234e
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs (2006, methodology): “ of Theorems E and F by using Theorem 2.2. Geometrically, our proof is built on the fact that the H U action on the Hermitian symmetric space is strongly visible if (G U,H U) is a symmetric pair (see [50]). 7.2 Representations associated to maximal parabolic subalgebras Let gC be a complex simple Li”