Conjugation on varieties of nilpotent matrices

Derivate 3019

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We consider the conjugation-action of an arbitrary upper-block parabolic subgroup P of the general linear group (over C) on the variety of x-nilpotent complex matrices. We obtain a criterion as to whether the action admits a finite number of orbits and specify systems of representatives for the orbits in all finite cases. Furthermore, we give a set-theoretic description of their closures and examine them for minimal degenerations in case x=2. Concerning the action on the nilpotent cone, we obtain a generic P-normal form of the orbits which yields generic normal forms for the actions of the Borel subgroup B of upper-triangular matrices and of the standard unipotent subgroup U of B. We describe generating (semi-) invariants for the Borel semi-invariant ring as well as for the U-invariant ring. The latter is examined in more detail in terms of algebraic quotients by a toric variety closely related.

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Dokumententyp:
Wissenschaftliche Abschlussarbeiten » Dissertation
Fakultäten und Einrichtungen:
Fakultät für Mathematik und Naturwissenschaften » Mathematik und Informatik » Dissertationen
Dewey Dezimal-Klassifikation:
500 Naturwissenschaften und Mathematik » 510 Mathematik » 510 Mathematik
Language:
Englisch
Collection / Status:
Dissertationen / Document published
Date of doctoral degree:
03.07.2012
Files changed on:
12.08.2014
Medientyp:
Text