Topic
Symplectic vector space
About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.
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TL;DR: In this article, it was shown that helicity is the moment map of duality acting as an SO ( 2 ) group of canonical transformations on the symplectic space of all solutions of the vacuum Maxwell equations.
8 citations
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TL;DR: In this article, the sets of conjugate matrices are classified and a representative of a not too difficult shape in each such set is found, assuming that K is contained in the field of complex numbers, and an intensive treatment is being done for certain real fields K because real symplectic groups are important in the theory of SlEGEL'S modular functions.
Abstract: The task of this paper is to classify the sets of conjugate matrices and to find a representative of a not too difficult shape in each such set. Throughout this paper we assume that K is contained in the field of complex numbers. An especially intensive treatment is being done for certain real fields K because real symplectic groups are important in the theory of SlEGEL'S modular functions. This paper was partially supported by an N.S.F. grant.
8 citations
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TL;DR: In this article, a simple interpretation of Gaiotto's construction in terms of derived symplectic geometry is given, where symplectic G-representations are replaced by arbitrary symplectic manifolds equipped with a Hamiltonian G-action and with an action of the multiplicative group that rescales the symplectic form with positive weight.
Abstract: Let BunG be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, Gaiotto (2016) associated to any symplectic representation of G a Lagrangian subvariety of T∗BunG. We give a simple interpretation of (a generalization of) Gaiotto’s construction in terms of derived symplectic geometry. This allows to consider a more general setting where symplectic G-representations are replaced by arbitrary symplectic manifolds equipped with a Hamiltonian G-action and with an action of the multiplicative group that rescales the symplectic form with positive weight.
8 citations
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TL;DR: In this article, the general theory for symplectic torus actions with symplectic or coisotropic orbits was applied to prove that a four-manifold with a symplectic two-torus action admits an invariant complex structure and gave an identification of those that do not admit a Kahler structure with Kodaira's class of complex surfaces which admit a nowhere vanishing holomorphic (2,0)-form, but are not a torus nor a K3 surface.
Abstract: We apply the general theory for symplectic torus actions with symplectic or coisotropic orbits to prove that a four-manifold with a symplectic two-torus action admits an invariant complex structure and give an identification of those that do not admit a Kahler structure with Kodaira's class of complex surfaces which admit a nowhere vanishing holomorphic (2,0)-form, but are not a torus nor a K3 surface.
8 citations
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TL;DR: In this article, the Riemann-Roch number of some of the pentagon spaces defined in [Kl], [KM], [HK1] was calculated and it was shown that the regular pentagon space is diffeomorphic to a toric variety, even symplectomorphic to one under arbitrarily small perturbations of its symplectic structure.
Abstract: We calculate the Riemann-Roch number of some of the pentagon spaces defined in [Kl], [KM], [HK1]. Using this, we show that while the regular pentagon space is diffeomorphic to a toric variety, even symplectomorphic to one under arbitrarily small perturbations of its symplectic structure, it does not admit a symplectic circle action. In particular, within the cohomology classes of symplectic structures, the subset admitting a circle action is not closed.
8 citations