
Journal of Lie Theory 22 (2012), No. 4, 10391048 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 mgualt@math.toronto.edu Patrick Hayden School of Computer Science, McGill University, Montreal, Canada patrick@cs.mcgill.ca We describe the orbit structure for the action of the centralizer group C(T) of a linear operator T on a finitedimensional complex vector space V. The main application is to the classification of solutions to a system of firstorder 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 [ Fulltextpdf (305 KB)] for subscribers only. 