Reversible Equivariant Linear Systems

In this paper we classify the structure of linear reversible systems (vector fields) on 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.