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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
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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Copyright information

© 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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