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Group theory --- p-adic fields. --- Groupes p-adiques. --- Symplectic groups. --- Groupes symplectiques. --- Representations of groups. --- Représentations de groupes. --- p-adic fields --- Representations of groups --- Symplectic groups --- Groups, Symplectic --- Linear algebraic groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Algebraic fields --- p-adic numbers

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Symplectic geometry. --- Symplectic groups. --- Domains of holomorphy. --- Géométrie symplectique. --- Groupes symplectiques. --- Domaines d'holomorphie. --- Géométrie symplectique --- Groupes symplectiques --- Domaines d'holomorphie --- Symplectic geometry --- Symplectic groups --- Domains of holomorphy --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Groups, Symplectic --- Linear algebraic groups --- Geometry, Differential

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Functional analysis --- Symplectic groups. --- Groupes symplectiques --- Trace formulas. --- Formules de trace --- Orbit method. --- Orbites, Méthode des --- Representations of groups. --- Représentations de groupes --- Orbit method --- Representations of groups --- Symplectic groups --- Trace formulas --- Formulas, Trace --- Automorphic forms --- Discontinuous groups --- Groups, Symplectic --- Linear algebraic groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Method of orbits --- Orbits, Method of --- Representations of algebras --- Groupes symplectiques. --- Formules de trace. --- Orbites, Méthode des. --- Représentations de groupes.

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One of the basic ideas in differential geometry is that the study of analytic properties of certain differential operators acting on sections of vector bundles yields geometric and topological properties of the underlying base manifold. Symplectic spinor fields are sections in an L^2-Hilbert space bundle over a symplectic manifold and symplectic Dirac operators, acting on symplectic spinor fields, are associated to the symplectic manifold in a very natural way. Hence they may be expected to give interesting applications in symplectic geometry and symplectic topology. These symplectic Dirac operators are called Dirac operators, since they are defined in an analogous way as the classical Riemannian Dirac operator known from Riemannian spin geometry. They are called symplectic because they are constructed by use of the symplectic setting of the underlying symplectic manifold. This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.

Symplectic geometry. --- Symplectic and contact topology. --- Symplectic groups. --- Dirac equation. --- Géométrie symplectique --- Topologie symplectique et de contact --- Groupes symplectiques --- Dirac, Equation de --- Symplectic geometry --- Symplectic and contact topology --- Symplectic groups --- Dirac equation --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Algebra --- Clifford algebras. --- Differential operators. --- Operators, Differential --- Geometric algebras --- Mathematics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Differential geometry. --- Differential Geometry. --- Global Analysis and Analysis on Manifolds. --- Differential geometry --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- Differential equations --- Operator theory --- Differential equations, Partial --- Quantum field theory --- Wave equation --- Algebras, Linear --- Global differential geometry. --- Global analysis. --- Global analysis (Mathematics) --- Groups, Symplectic --- Linear algebraic groups --- Topology, Symplectic and contact

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Symplectic groups --- Representations of groups --- Forms, Modular --- 514.76 --- Lifting theory --- Maslov index --- Series, Theta --- Groups, Symplectic --- Linear algebraic groups --- Theta series --- Functions, Theta --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Index, Maslov --- Forms, Quadratic --- Lagrangian functions --- Vector spaces --- Measure theory --- Modular forms --- Forms (Mathematics) --- Geometry of differentiable manifolds and of their submanifolds --- 514.76 Geometry of differentiable manifolds and of their submanifolds --- Nombres, Théorie des --- Formes automorphes --- Number theory --- Automorphic forms --- Fonctions thêta --- Opérateurs pseudo-différentiels --- Functions, Theta. --- Number theory. --- Fonctions thêta. --- Nombres, Théories des --- Opérateurs pseudo-différentiels --- Analyse sur une variété