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Let  be an exceptional simple algebraic group, and let  be a maximal torus in . In this paper, for every such , we find all simple rational -modules  with the following property: for every vector  ∈ , the closure of its -orbit is a normal affine variety. To solve this problem, we use a combinatorial criterion of normality formulated in terms of weights of simple -modules. This paper continues the works of the second author in which the same problem was solved for classical linear groups.

Simple modules of exceptional groups with normal closures of maximal torus orbits