%0 Journal Article
%T B-orbits of 2-nilpotent matrices and generalizations
%A Magdalena Boos
%A Markus Reineke
%J Mathematics
%D 2010
%I arXiv
%X The orbits of the group B of upper-triangular matrices acting on 2-nilpotent complex matrices via conjugation are classified via oriented link patterns, generalizing A. Melnikov's classification of the B-orbits on upper-triangular such matrices. The orbit closures as well as the "building blocks" of minimal degenerations of orbits are described. The classification uses the theory of representations of finite-dimensional algebras. Furthermore, we initiate the study of the B-orbits on arbitrary nilpotent matrices.
%U http://arxiv.org/abs/1004.1996v1