Algebras and Representation Theory

, Volume 17, Issue 6, pp 1683–1706 | Cite as

Non-Reductive Conjugation on the Nilpotent Cone

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Abstract

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of GLn(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.

Keywords

Parabolic orbits in the nilpotent cone Semiinvariants Generic normal form (Semi-)invariant ring 

Mathematics Subject Classifications (2010)

14R20 16W22 

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Fachbereich C - MathematikBergische Universität WuppertalWuppertalGermany

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