Coisotropic Pairs

TL;DR

This paper introduces a classification framework for pairs of coisotropic subspaces in symplectic vector spaces, providing invariants and elementary types to understand their structure.

Contribution

It presents two equivalent sets of invariants for classifying coisotropic pairs and decomposes any such pair into elementary types.

Findings

Two sets of invariants classify coisotropic pairs.

Any coisotropic pair decomposes into elementary types.

Identification of five elementary types of coisotropic pairs.

Abstract

We give two equivalent sets of invariants which classify pairs of coisotropic subspaces of a finite-dimensional symplectic vector space. We identify five elementary types of coisotropic pairs and show that any coisotropic pair decomposes in an appropriate sense as the direct sum of coisotropic pairs of elementary type.