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Journal of Lie Theory 22 (2012), No. 4, 1039--1048
Copyright Heldermann Verlag 2012

Orbits of the Centralizer of a Linear Operator

Paul Best
Warburg Pincus LLC, London, England

Marco Gualtieri
Dept. of Mathematics, University of Toronto, Bahen Centre, 40 St. George Street, Toronto M5S 2E4, Canada

Patrick Hayden
School of Computer Science, McGill University, Montreal, Canada

We describe the orbit structure for the action of the centralizer group C(T) of a linear operator T on a finite-dimensional complex vector space V. 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.

Keywords: Centralizer, classification of solutions, orbit lattice.

MSC: 15A21, 34A30

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