@article{16633,
abstract = {AbstractWe obtain normal forms for infinitesimally symplectic matrices (or linear Hamiltonian vector fields) that commute with the symplectic action of a compact Lie group of symmetries. In doing so we extend Williamson's theorem on normal forms when there is no symmetry present.Using standard representation-theoretic results the symmetry can be factored out and we reduce to finding normal forms over a real division ring. There are three real division rings consisting of the real, complex and quaternionic numbers. Of these, only the real case is covered in Williamson's original work.},
author = {Melbourne, Ian and Dellnitz, Michael},
issn = {0305-0041},
journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
pages = {235--268},
title = {{Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}},
doi = {10.1017/s0305004100071577},
year = {1993},
}