Lectures on Gaussian integral operators and classical groups

DOI10.4171/080zbMath1211.22001OpenAlexW1499013296MaRDI QIDQ627318

Yuriĭ A. Neretin

Publication date: 28 February 2011

Published in: EMS Series of Lectures in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/080

zbMATH Keywords

Fock spacesZak transformSegal-Bargmann transformclassical \(p\)-adic groupspseudo-Euclidean geometryCartier modelGaussian \(p\)-adic operatorsGaussian integral operatorsgroups U\((p, q)\)Hilbert spaces of holomorphic functions in matrix ballslinear symplectic geometryoperators with theta-kernelsreal-adelic correspondenceWeil representation over \(p\)-adic field

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Integral operators (47G10) Differential geometry of symmetric spaces (53C35) Representations of Lie and linear algebraic groups over local fields (22E50) Research exposition (monographs, survey articles) pertaining to topological groups (22-02) Linear operators on spaces with an indefinite metric (47B50)

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