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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01 Jan 1991
TL;DR: In this article, it was shown that by taking stationary flows of integrable evolution equations on lattices, one obtains integrably symplectic maps and an alternative method based on the so-called nonlinearization of a scattering problem, and elucidate its intimate connections with the previous one.
Abstract: We show that by taking stationary flows of integrable evolution equations on lattices one obtains integrable symplectic maps. We also tersely discuss an alternative method based on the so-called nonlinearization of a scattering problem, and elucidate its intimate connections with the previous one. A few examples of possibly interesting integrable maps are presented.
12 citations
TL;DR: The restricted symplectic group is defined for an infinite-dimensional symplectic space over the field Qp of p-adic numbers in this article, and an expression for the cocycle of this representation is given in terms of the padic Maslov index.
Abstract: An analogue of the Fock representation is constructed for the infinite-dimensional p-adic Heisenberg group.The restricted symplectic group is defined for an infinite-dimensional symplectic space over the field Qp of p-adic numbers. For the restricted symplectic group a projective representation is constructed that is compatible with the representation of the Heisenberg group, and an expression for the cocycle of this representation is given in terms of the p-adic Maslov index. It is proved that the extension corresponding to this cocycle reduces to a Z2-extension.
12 citations
TL;DR: In this paper, the authors give a systematic treatment of the construction of coherent states associated to compact integral symplectic manifolds by geometric quantization and collect some recent results about the properties of such coherent states.
12 citations
TL;DR: In this paper, it was shown that given four arbitrary quaternion numbers of norm 1 there always exists a 2 × 2 symplectic matrix for which those numbers are left eigenvalues.
12 citations
TL;DR: In this article, the authors classify all multiplicity free representations of G-invariant symplectic representations and show that all of them are commutative, i.e., the ring O(V ) G of invariants is a sub-Poisson algebra.
12 citations