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
01 Mar 2013
TL;DR: In this paper, the uniqueness questions for symplectic forms on compact manifolds without boundary are discussed, and a survey paper discusses some uniqueness problems for compact manifold without boundary is presented.
Abstract: This survey paper discusses some uniqueness questions for symplectic forms on compact manifolds without boundary.
44 citations
TL;DR: In this paper, a double compactified D=11 supermembrane with nontrivial wrapping was formulated as a symplectic non-commutative gauge theory on the world volume.
Abstract: It is shown that a double compactified D=11 supermembrane with nontrivial wrapping may be formulated as a symplectic noncommutative gauge theory on the world volume The symplectic noncommutative structure is intrinsically obtained from the symplectic two-form on the world volume defined by the minimal configuration of its Hamiltonian The gauge transformations on the symplectic fibration are generated by the area preserving diffeomorphisms on the world volume Geometrically, this gauge theory corresponds to a symplectic fibration over a compact Riemann surface with a symplectic connection
44 citations
TL;DR: In this paper, a uniqueness theorem for an analogue of the Bessel model of an irreducible representation of a symplectic group of rank 2 over a disconnected local field is proved.
Abstract: In this paper we prove a uniqueness theorem for an analogue of the Bessel model of an irreducible representation of a symplectic group of rank 2 over a disconnected local field. Bibliography: 4 items.
44 citations
01 Jan 1976
TL;DR: In this paper, Souriau defined the moment of a Lie group action as a suitable map J : M → G* (dual of the Lie algebra G of G) for which J −1(ξ) quotiented by the action of the isotropy subgroup of ξ is a symplectic manifold.
Abstract: Let (M, ω) be a symplectic manifold and G a Lie group acting on M by symplectic diffeomorphisms (i.e. g*ω = ω for all g ∈ G). Souriau has defined the moment of this group action as a suitable map J : M → G* (dual of the Lie algebra G of G). Some well-known results are first briefly outlined in Part I: there exists an action of G on G* for which J is equivariant, whose orbits ϑξ are symplectic manifolds (Kirillov-Souriau-Kostant’s theorem); if ξ is a regular value of J, J −1(ξ) quotiented by the action of the isotropy subgroup of ξ is, under suitable assumptions, a symplectic manifold (Meyer’s theorem).
44 citations
TL;DR: In this paper, a generalized fixed-point problem was considered from the point of view of some relatively recently discovered symplectic rigidity phenomena, which has interesting applications concerning global perturbations of Hamiltonian systems.
Abstract: In this paper we study a generalized symplectic fixed-point problem, first considered by J. Moser in [20], from the point of view of some relatively recently discovered symplectic rigidity phenomena. This problem has interesting applications concerning global perturbations of Hamiltonian systems. © 2007 Wiley Periodicals, Inc.
44 citations