Non-Reductive Conjugation on the Nilpotent Cone

Abstract

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of ${\mathrm{GL}}_n(\mathbf{C})$, especially of the Borel subgroup $B$ and of the standard unipotent subgroup $U$ 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 $U$-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.

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

References in corpus (2)

• Conjugation on varieties of nilpotent matrices
• Non-Reductive Conjugation on the Nilpotent Cone

Cited by in corpus (1)

• Non-Reductive Conjugation on the Nilpotent Cone