Jeroen S.W. Lamb & Mark Roberts:

Reversible equivariant linear systems

abstract:

In this paper we classify the structure of linear reversible systems
(vector fields) on $\RR^n$ that are equivariant with respect
to a linear representation of a compact Lie group $H$. We assume the
time-reversal symmetry $R$ also acts linearly and is such that the
group $G$ that is generated by $H$ and $R$ is again a compact Lie
group. The main tool for the classification is the representation theory
of compact Lie groups. The results are applied to some generic eigenvalue
movements of linear reversible equivariant systems.