(Co)isotropic Pairs in Poisson and Presymplectic Vector Spaces

TL;DR

This paper classifies pairs of coisotropic subspaces in Poisson vector spaces using two equivalent sets of invariants, employing duality with presymplectic spaces and identifying fundamental elementary types.

Contribution

It introduces a novel classification framework for pairs of coisotropic subspaces via invariants and elementary types, with an explicit invertible matrix relating these invariants.

Findings

Two equivalent invariant sets classify pairs of coisotropic subspaces.

Identification of ten elementary types as building blocks.

An explicit invertible matrix relates the invariants.

Abstract

We give two equivalent sets of invariants which classify pairs of coisotropic subspaces of finite-dimensional Poisson vector spaces. For this it is convenient to dualize; we work with pairs of isotropic subspaces of presymplectic vector spaces. We identify ten elementary types which are the building blocks of such pairs, and we write down a matrix, invertible over $\mathbb{Z}$, which takes one 10-tuple of invariants to the other.