Simple Modules of Exceptional Groups with Normal Closures of Maximal   Torus Orbits
  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. 
Ilya I. Bogdanov, Karine G. Kuyumzhiyan
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