Spineurs symplectiques purs et indice de Maslov de plans lagrangiens positifs

DOI10.1016/0022-1236(84)90054-5zbMath0548.57024OpenAlexW2046548823MaRDI QIDQ799274

Bernard Magneron

Publication date: 1984

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(84)90054-5

zbMATH Keywords

group extensionsMaslov indexmetaplectic groupShilov boundary2-cocyclescanonical intertwining operatorsholomorphically induced representation of the Heisenberg groupmanifold of pure symplectic spinorspositive Lagrangian submanifoldsspin representation of the Clifford algebratransformation space extensiontransformation spacesuniversal covering of the symplectic group

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Characteristic classes and numbers in differential topology (57R20) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Spin and Spin({}^c) geometry (53C27)

Related Items

Cohomologie des groupes et des espaces de transformation. (Group cohomology and transformation spaces) ⋮ Geometric quantization, parallel transport and the Fourier transform ⋮ The generalized Maslov index ⋮ GEOMETRIC PHASES IN THE QUANTISATION OF BOSONS AND FERMIONS ⋮ The Maslov triple index on the Shilov boundary of a classical domain ⋮ Representations of a solvable Lie group on \({\bar \partial}_ b\) cohomology spaces ⋮ The Maslov index revisited

Cites Work

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• Unitary representations of some infinite dimensional groups
• Algèbre de Clifford symplectique, revetements du groupe symplectique, indices de Maslov et spineurs symplectiques
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• Polarization and unitary representations of solvable Lie groups. Appendix by Calvin C. Moore
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• On a Hilbert space of analytic functions and an associated integral transform part I
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• À propos de l'article «Sur la cohomologie réelle des groupes de Lie simples réels»
• Linear Symmetries of Free Boson Fields
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