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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TL;DR: In this paper, the full classification of invariant symplectic, (almost) complex and Kahler structures, together with their paracomplex analogues, on four-dimensional pseudo-Riemannian generalized symmetric spaces was obtained.
Abstract: We obtain the full classification of invariant symplectic, (almost) complex and Kahler structures, together with their paracomplex analogues, on four-dimensional pseudo-Riemannian generalized symmetric spaces. We also apply these results to build some new examples of five-dimensional homogeneous K -contact, Sasakian, K -paracontact and para-Sasakian manifolds.
11 citations
TL;DR: In this paper, both the finite and infinite characters of the inductive limit symplectic group G are classified using a multiplicative structure on an ordered completion of the K0-group for the group C ∗-algebra A of G. The authors also give explicit examples of the k-theory for certain primitive quotients of A.
11 citations
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TL;DR: In this article, the authors generalize Fujiki relation of Beauville-Bogomolov quadratic form on a projective symplectic variety as an application, and study a fibre space structure of a projectively-symmetric variety.
Abstract: We generalize Fujiki relation of Beauville-Bogomolov quadratic form on a projective symplectic variety As an application, we study a fibre space structure of a projective symplectic variety
11 citations
01 Jan 2002
TL;DR: In this article, an index function theory for paths in the symplectic groups started from the identity was introduced, i.e., elements in Pτ(2n) with τ > 0 defined by (2.0.
Abstract: In this chapter, we introduce an index function theory for paths in the symplectic groups started from the identity, i.e., elements in Pτ(2n) with τ > 0 defined by (2.0.1):
. For τ> 0 and ω∈U, we further define the set of ω-non-degenerate paths by
(1)
and the set of ω-degenerate paths by
(2)
.
11 citations
TL;DR: In this article, the Hilbert-Chow morphism was used to construct a canonical desingularization of the symplectic reduction, which is isomorphic to the closure of a nilpotent orbit in a simple Lie algebra.
Abstract: Let $$G \subset GL(V)$$
be a reductive algebraic subgroup acting on the symplectic vector space $$W=(V \oplus V^*)^{\oplus m}$$
, and let $$\mu :\ W \rightarrow Lie(G)^*$$
be the corresponding moment map. In this article, we use the theory of invariant Hilbert schemes to construct a canonical desingularization of the symplectic reduction $$\mu ^{-1}(0)/\!/G$$
for classes of examples where $$G=GL(V)$$
, $$O(V)$$
, or $$Sp(V)$$
. For these classes of examples, $$\mu ^{-1}(0)/\!/G$$
is isomorphic to the closure of a nilpotent orbit in a simple Lie algebra, and we compare the Hilbert–Chow morphism with the (well-known) symplectic desingularizations of $$\mu ^{-1}(0)/\!/G$$
.
11 citations