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arXiv · 1504.05374

Non-Reductive Conjugation on the Nilpotent Cone

Magdalena Boos
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Abstract

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of ${\rm GL}_n(\mathbf{C})$, 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.

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Magdalena Boos. 2015-04-21. Non-Reductive Conjugation on the Nilpotent Cone. https://doi.org/10.1007/s10468-014-9465-z

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