Orbits of the Centralizer of a Linear Operator

Details Orbits of the Centralizer of a Linear Operator Orbits of the Centralizer of a Linear Operator

2011-10-21

arxiv.org/abs/1110.4899v1

Mathematics

Dynamical Systems

10 pages. To appear in Journal of Lie Theory

Scientific paper

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.

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