Geodesic
Orbits of the Centralizer of a Linear Operator
Journal of Lie theory, Tome 22 (2012) no. 4, pp. 1039-1048
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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.
Classification : 15A21, 34A30
Mots-clés : Centralizer, classification of solutions, orbit lattice 
@article{JLT_2012_22_4_JLT_2012_22_4_a4,
     author = {P. Best and M. Gualtieri and P. Hayden},
     title = {Orbits of the {Centralizer} of a {Linear} {Operator}},
     journal = {Journal of Lie theory},
     pages = {1039--1048},
     year = {2012},
     volume = {22},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2012_22_4_JLT_2012_22_4_a4/}
}
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P. Best; M. Gualtieri; P. Hayden. Orbits of the Centralizer of a Linear Operator. Journal of Lie theory, Tome 22 (2012) no. 4, pp. 1039-1048. http://geodesic.mathdoc.fr/item/JLT_2012_22_4_JLT_2012_22_4_a4/