Algebras and Representation Theory

, Volume 17, Issue 6, pp 1657–1682 | Cite as

Finite Parabolic Conjugation on Varieties of Nilpotent Matrices

Article

Abstract

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of GLn(C) on the variety of x-nilpotent complex matrices and translate it to a representation-theoretic context. We obtain a criterion as to whether the action admits a finite number of orbits and specify a system of representatives for the orbits in the finite case of 2-nilpotent matrices. Furthermore, we give a set-theoretic description of their closures and specify the minimal degenerations in detail for the action of the Borel subgroup. We show that in all non-finite cases, the corresponding quiver algebra is of wild representation type.

Keywords

Parabolic orbits of nilpotent matrices Degenerations Finite classification 

Mathematics Subject Classification (2010)

16G20 16G60 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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