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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, a study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated, and the influence of an effective action of a K3 group via symplectic symmetry is investigated.
Abstract: A study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated. A measurement of exoticness of a symplectic homotopy K3 surface is introduced, and the influence of an effective action of a K3 group via symplectic symmetries is investigated. It is shown that an effective action by various maximal symplectic K3 groups forces the corresponding homotopy K3 surface to be minimally exotic with respect to our measure. (However, the standard K3 is the only known example of such minimally exotic homotopy K3 surfaces.) The possible structure of a finite group of symplectic symmetries of a minimally exotic homotopy K3 surface is determined and future research directions are indicated.
10 citations
Posted Content•
TL;DR: In this article, the double covering of the metaplectic group of the symplectic vector space was studied and the representation of G˜ on the space of exterior forms was given.
Abstract: Let λ : G˜ → Gbe the non-trivial double covering of the symplectic groupG= Sp(V,ω) of the symplectic vector space (V,ω) by the metaplectic groupG˜ = Mp(V,ω).In this case, λis also a representation of G˜ on the vector spaceV and thus, it gives rise to the representation of G˜ on the space of exteriorformsV
10 citations
TL;DR: In this article, it was shown that it is possible to define canonical Dirac operators acting on symplectic spinor fields in a similar way as one knows it from the Dirac operator on Riemannian manifolds.
Abstract: The notion of symplectic spinors over a symplectic manifold was already introduced by B. Kostant in 1974 as a tool in his theory of geometric quantization. We observed that it is possible to define canonical symplectic Dirac operators acting on symplectic spinor fields in a similar way as one knows it from the Dirac operator on Riemannian manifolds. In this paper we study symplectic Dirac operators provided that the underlying manifold is a Kahler manifold with the Kahler form as symplectic structure.
9 citations
TL;DR: In this article, an expression of the so(4,2) algebra on a six-dimensional symplectic manifold, in terms of the generators defined on this manifold, is obtained, which coincides with the symplectic form introduced by Kirillov Kostant and Souriau, given a Darboux expression with the aid of three pairs of canonically conjugated variables.
Abstract: On each six‐dimensional symplectic manifold a coordinate‐free realization of the so(4,2) algebra can be constructed, the generators of which satisfy the polynomial relations fulfilled by the so(4,2) generators associated with the Kepler problem. This realization contains as a particular case several realizations of so(4,2) known in the literature. An expression of the symplectic form on a six‐dimensional symplectic manifold, in terms of the so(4,2) generators defined on this manifold, is obtained. In particular, on the six‐dimensional orbit of the SO(4,2) group in so(4,2) this symplectic form coincides with the symplectic form introduced by Kirillov Kostant and Souriau. The symplectic form is given a Darboux expression with the aid of three pairs of canonically conjugated variables, which are a generalization of the Delaunay elements defined in the Kepler problem.
9 citations
TL;DR: In this article, it was shown that the kernels of the restrictions of Dirac-Dolbeault operators on natural subspaces of polynomial valued spinor fields are finite dimensional on a compact symplectic manifold.
9 citations