On the maximum nilpotent orbit which intersects the centralizer of a matrix
Abstract
We introduce a method to determine the maximum nilpotent orbit which intersects a variety of nilpotent matrices described by a strictly upper triangular matrix over a polynomial ring. We show that the result only depends on the ranks of its submatrices and we introduce conditions on a subvariety so that it intersects the same orbit. Then we describe a maximal nilpotent subalgebra of the centralizer of any nilpotent matrix; the previous method allows us to show that the maximum nilpotent orbit which intersects that centralizer only depends on which entries are identically 0 in that subalgebra. The aim of the paper is to prove a simple algorithm for the determination of the maximum nilpotent orbit which intersects that centralizer, which was conjectured by Polona Oblak.
Cite
@article{arxiv.1710.03588,
title = {On the maximum nilpotent orbit which intersects the centralizer of a matrix},
author = {Roberta Basili},
journal= {arXiv preprint arXiv:1710.03588},
year = {2017}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1202.3369