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16. 12. 2022.
Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size
In this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix $B$ consisting of two Jordan blocks of the same size. We list all the possible Jordan canonical forms of the nilpotent matrices that commute with $B$ by characterizing the corresponding partitions.