Mathematical Notes

, Volume 92, Issue 3–4, pp 445–457 | Cite as

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

  • I. I. BogdanovEmail author
  • K. G. Kuyumzhiyan


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.


variety normality irreducible representation exceptional group maximal torus weight decomposition 


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© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyMoscowrussia
  2. 2.National Research University “Higher School of Economics,”MoscowRussia

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