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
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 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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