Finite Parabolic Conjugation on Varieties of Nilpotent Matrices
Abstract
We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of on the variety of -nilpotent complex matrices and translate it to a representation-theoretic context. We obtain a criterion as to whether the action admits a finite number of orbits and specify a system of representatives for the orbits in the finite case of -nilpotent matrices. Furthermore, we give a set-theoretic description of their closures and specify the minimal degenerations in detail for the action of the Borel subgroup. We show that in all non-finite cases, the corresponding quiver algebra is of wild representation type.
Keywords
Cite
@article{arxiv.1504.05367,
title = {Finite Parabolic Conjugation on Varieties of Nilpotent Matrices},
author = {Magdalena Boos},
journal= {arXiv preprint arXiv:1504.05367},
year = {2015}
}
Comments
The final publication is available at http://link.springer.com/article/10.1007%2Fs10468-014-9464-0#. arXiv admin note: substantial text overlap with arXiv:1205.5197