Geometry of orbit closures for the representations associated to gradings of Lie algebras of types $E_7$

Abstract

This paper is a continuation of arXiv:1201.1102. We investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on the simple Lie algebra of type $E_7$. The methods for classifying the orbits for these actions were developed by Vinberg . We give the orbit descriptions, the degeneration partial orders, and indicate normality of the orbit closures. We also investigate the rational singularities, Cohen-Macaulay and Gorenstein properties for the orbit closures. We give the information on the defining ideals of orbit closures.

arXiv admin note: substantial text overlap with arXiv:1201.1102 some corrections in degeneration orders

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