摘要: We show that for n>=3 the symplectic group Sp(n) is as a 2-compact group determined up to isomorphism by the isomorphism type of its maximal torus normalizer. This allows us to determine the integral homotopy type of Sp(n) among connected finite loop spaces with maximal torus....
This interesting article is connected with the following problem by the reviewer: describe the lattice of those subgroups of a given classical group of matrices over a ring which contain the subgroup formed by matrices with coefficients in some subring [see: Yu. I. Merzlyakov, Itogi Nauki. ...
Let G be a connected Lie group with Lie algebra g, and let O be the coadjoint orbit through the element g∈g * . Further, let h be a real polarization at g, and let F be the corresponding G-invariant polarization of the symplectic manifold O. In this situation the space F 1 (O...
Therefore, this finiteness reflects certain finiteness of the automorphism group of a variety, and it seems to be most interesting when the Kodaira dimension of X is 0. The main theorem of this paper is the following. Theorem 1.0.1 (Theorem 3.1.2, Theorem 4.3.6) Let k'/k be a finite...
we will review what we do and do not know\nabout the existence and uniqueness of smooth and symplectic structures on\nclosed, simply connected 4-manifol... R Fintushel,RJ Stern - arXiv Mathematics e-prints 被引量: 0发表: 2006年 GENERALIZED BESSEL MODELS FOR A SYMPLECTIC GROUP OF RANK ...
Thecircle groupU (1), also known as first unitary group, is the one-dimensional Lie group of complex numbers of unit modulus with the standard multiplication operation. It can be parametrized viae^{i\theta }for\theta \in [0,2\pi ), and is isomorphic to the special orthogonal group\text...
All the symplectic matrices possessing a fixed eigenvalue ω on the unit circle form ahypersurface in the real symplectic group Sp(2n). This paper is devoted to the study of the topologicalstructures of this hypersurface and its complement in Sp(2n).关键词: Symplectic groups ω-subsets Toplogic...
Let (M,\\omega) be a four dimensional compact connected symplectic manifold.We prove that (M,\\omega) admits only finitely many inequivalent Hamiltonianeffective 2-torus actions. Consequently, if M is simply connected, the numberof conjugacy classes of 2-tori in the symplectomorphism group ...
We hereafter assumeGto be a connected Lie group with a Lie algebra\mathfrak {g}. Let us set some definitions and conventions concerning Lie group actions. If\Phi : G\times P\rightarrow Pis a Lie group action and\Phiis known from the context or its explicit form is irrelevant, we will...
The aim of the author is to classify the following three structures: (1) connected partial linear spaces whose subspaces are dual affine planes of order 2. (2) connected graphs in which the neighbourhood of any vertex x is a grid graph L... Hall,J. I. - 《Proceedings of the London ...