Geometry of orbit closures for the representations associated to gradings of Lie algebras of types $E_6$, $F_4$ and $G_2$
Abstract
In this paper we investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on a simple Lie algebras of type $E_6$, $F_4$ and $G_2$. The methods for classifying the orbits for these actions were developed by Vinberg. We give the orbit descriptions, the degeneration partial orders, and decide the normality of the orbit closures. We also investigate the rational singularities, CohenMacaulay and Gorenstein properties for the orbit closures. We give the generators of the defining ideals of orbit closures.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 arXiv:
 arXiv:1201.1102
 Bibcode:
 2012arXiv1201.1102K
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Geometry;
 22E55;
 14M17