Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits

Details Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits

2011-05-23

arxiv.org/abs/1105.4577v1

Mathematics

Algebraic Geometry

Scientific paper

Let G be an exceptional simple algebraic group, and let T be a maximal torus in G. In this paper, for every such G, we find all simple rational G-modules V with the following property: for every vector v in V, the closure of its T-orbit is a normal affine variety. For all G-modules without this property we present a T-orbit with the non-normal closure. To solve this problem, we use a combinatorial criterion of normality formulated in the terms of weights of a simple G-module. This paper continues two papers of the second author, where the same problem was solved for classical linear groups.

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