Non-Reductive Conjugation on the Nilpotent Cone
Representation Theory
2015-04-22 v1 Algebraic Geometry
Abstract
We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of , especially of the Borel subgroup and of the standard unipotent subgroup of the latter on the nilpotent cone of complex nilpotent matrices. We obtain generic normal forms of the orbits and describe generating (semi-) invariants for the Borel semi-invariant ring as well as for the -invariant ring. The latter is described in more detail in terms of algebraic quotients by a special toric variety closely related. The study of a GIT-quotient for the Borel-action is initiated.
Cite
@article{arxiv.1504.05374,
title = {Non-Reductive Conjugation on the Nilpotent Cone},
author = {Magdalena Boos},
journal= {arXiv preprint arXiv:1504.05374},
year = {2015}
}
Comments
The final publication is available at http://link.springer.com/article/10.1007%2Fs10468-014-9465-z. arXiv admin note: substantial text overlap with arXiv:1205.5197