Mathematical Notes

, Volume 92, Issue 3–4, pp 445–457

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

• I. I. Bogdanov
• K. G. Kuyumzhiyan
Article

## Abstract

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 vV, the closure of its T-orbit is a normal affine variety. To solve this problem, we use a combinatorial criterion of normality formulated in terms of weights of simple G-modules. This paper continues the works of the second author in which the same problem was solved for classical linear groups.

## Keywords

variety normality irreducible representation exceptional group maximal torus weight decomposition

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