Orbits of the Centralizer of a Linear Operator
arXiv:1110.4899
Abstract
We describe the orbit structure for the action of the centralizer group of a linear operator on a finite-dimensional complex vector space. The main application is to the classification of solutions to a system of first-order ODEs with constant coefficients. We completely describe the lattice structure on the set of orbits and provide a generating function for the number of orbits in each dimension.
10 pages. To appear in Journal of Lie Theory