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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 paper, a universal construction of a Lefschetz pencil with infinite fundamental groups is given for the case of Riemann surfaces with positive self-intersection and a small image of the fundamental group inside the ambient symplectic fourfold.
12 citations
TL;DR: In this article, Globally irreducible representations of the finite symplectic group Sp4(q) have been proposed for the first time in the context of communication in algebra.
Abstract: (1994). Globally irreducible representations of the finite symplectic group Sp4(q) Communications in Algebra: Vol. 22, No. 15, pp. 6439-6457.
12 citations
TL;DR: Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.
Abstract: The structure of symplectic integrators up to fourth order can be completely and analytically understood when the factorization (split) coefficients are related linearly but with a uniform nonlinear proportional factor. The analytic form of these extended-linear symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and nonforward fourth-order algorithms with an arbitrary number of operators. Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.
12 citations
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TL;DR: In this paper, the authors compute the signatures of those symplectic Lefschetz fibra-tions and compute new words in the mapping class group, hence new SFLF signatures.
Abstract: The well-known fact that any genus g symplectic Lefschetz fibra- tion X 4 ! S 2 is given by a word that is equal to the identity element in the mapping class group and each of whose elements is given by a positive Dehn twist, provides an intimate relationship between words in the mapping class group and 4-manifolds that are realized as symplectic Lefschetz fibra- tions. In this article we provide new words in the mapping class group, hence new symplectic Lefschetz fibrations. We also compute the signatures of those symplectic Lefschetz fibrations.
12 citations
TL;DR: Using Proctor's sl(2, C) technique, it is proved that these symplectic lattices are rank symmetric, rank unimodal, and strongly Sperner.
12 citations