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.

Classification of symmetric caustics I: symplectic equivalence

Abstract: We generalise the classification theory of Arnold and Zakalyukin for singularities of Lagrange projections to projections that commute with a symplectic action of a compact Lie group. The theory is applied to the classification of infinitesimally stable corank 1 projections with ℤ2 symmetry. However examples show that even in very low dimensions there exist generic projections which are not infinitesimally stable.

Noncommutative differential forms and quantization of the odd symplectic category

Abstract: There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for all functions f and g. We notice that this noncommutative differential algebra has a geometrical realization as a convolution algebra of the symplectic groupoid integrating the Poisson manifold. This quantization is just a part of a quantization of the odd symplectic category (where objects are odd symplectic supermanifolds and morphisms are Lagrangian relations) in terms of 2-graded chain complexes. It is a straightforward consequence of the theory of BV operator acting on semidensities, due to H. Khudaverdian.

The most degenerate irreducible representations of the symplectic group

Abstract: Matrix elements of the generators of the symplectic group Sp(2n) have been obtained for the most degenerate irreducible representations (m2n,?) and (?2n). These are the only two cases for n≳2 where the state labels according to the branching laws of Hegerfeldt give rise to an orthogonal set of basic vectors.

Toric symplectic ball packing

Abstract: We define and solve the toric version of the symplectic ball packing problem, in the sense of listing all 2n-dimensional symplectic-toric manifolds which admit a perfect packing by balls embedded in a symplectic and torus equivariant fashion. In order to do this we first describe a problem in geometric-combinatorics which is equivalent to the toric symplectic ball packing problem. Then we solve this problem using arguments from Convex Geometry and Delzant theory. Applications to symplectic blowing-up are also presented, and some further questions are raised in the last section.