Geodesic
Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits
Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 483-496

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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. 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, weight decomposition.
Mots-clés : exceptional group, maximal torus 
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     author = {I. I. Bogdanov and K. G. Kuyumzhiyan},
     title = {Simple {Modules} of {Exceptional} {Groups} with {Normal} {Closures} of {Maximal} {Torus} {Orbits}},
     journal = {Matemati\v{c}eskie zametki},
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I. I. Bogdanov; K. G. Kuyumzhiyan. Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits. Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 483-496. http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a0/