Ornstein-Uhlenbeck operators and holomorphic representations for a class of bounded symmetric domains

DOI10.1016/j.bulsci.2023.103306MaRDI QIDQ6134704

Hélène Airault, Abdelhamid Boussejra

Publication date: 22 August 2023

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

zbMATH Keywords

symplectic groupCartan domainsOrnstein-Uhlenbeck operatorsBerezinian representation

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Homogeneous complex manifolds (32M10)

Cites Work

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• Lifted infinitesimal holomorphic representation for the \(n\)-dimensional complex hyperbolic ball and for Cartan domains of type I
• Unitarising measures for the representations of affine group and associated invariant operators
• Identities for vector fields in the infinitesimal representation of the symplectic group into the Siegel disk of complex symmetric matrices
• Function theory in the unit ball of \({\mathbb{C}}^ n\)
• Stochastic calculus of variations on complex line bundle and construction of unitarizing measures for the Poincaré disk
• Invariant or quasi-invariant probability measures for infinite dimensional groups. II: Unitarizing measures or Berezinian measures
• The Hua operators on bounded symmetric domains of tube type
• \(L^2\)-concrete spectral analysis of the invariant Laplacian \(\Delta_{\alpha\beta}\) in the unit complex ball \(B^n\)
• Unitarizing probability measures for representations of Virasoro algebra
• Analysis and geometry on complex homogeneous domains
• Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension
• QUANTIZATION IN COMPLEX SYMMETRIC SPACES