TY - JOUR
AB - 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.
AU - Melbourne, Ian
AU - Dellnitz, Michael
ID - 16633
JF - Mathematical Proceedings of the Cambridge Philosophical Society
SN - 0305-0041
TI - Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group
ER -