English

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 GLn(C){\rm GL}_n(\mathbf{C}), especially of the Borel subgroup BB and of the standard unipotent subgroup UU 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 UU-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.

Keywords

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

R2 v1 2026-06-22T09:19:40.228Z