On symplectic representations of normal \(j\)-algebras and their application to Xu's realizations of Siegel domains

DOI10.1016/j.difgeo.2006.02.001zbMath1156.17300OpenAlexW2154496001WikidataQ115357863 ScholiaQ115357863MaRDI QIDQ864876

Hideyuki Ishi

Publication date: 13 February 2007

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2006.02.001

zbMATH Keywords

symplectic representationSiegel domainnormal \(j\)-algebrareal solvable Lie algebra

Mathematics Subject Classification ID

Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Solvable, nilpotent (super)algebras (17B30) Homogeneous complex manifolds (32M10)

Related Items (8)

Wishart laws and variance function on homogeneous cones ⋮ Riesz measures and Wishart laws associated to quadratic maps ⋮ Tube domain and an orbit of a complex triangular group ⋮ Functional equations of zeta functions associated with homogeneous cones ⋮ Basic relative invariants of homogeneous cones and their Laplace transforms ⋮ Bergman kernel function for Hartogs domains over bounded homogeneous domains ⋮ Quotients of bounded homogeneous domains by cyclic groups ⋮ Characterization of the Riesz exponential family on homogeneous cones

Cites Work

• Representations of certain solvable Lie groups on Hilbert spaces of holomorphic functions and the application to the holomorphic discrete series of a semisimple Lie group
• Positive Riesz distributions on homogeneous cones
• Classification of homogeneous bounded domains of lower dimension
• Holomorphic Imbeddings of Symmetric Domains into a Siegel Space
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