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Siberian Mathematical Journal

, Volume 53, Issue 6, pp 1089–1104 | Cite as

Simple modules of classical linear groups with normal closures of maximal torus orbits

  • K. G. KuyumzhiyanEmail author
Article

Abstract

Let T be a maximal torus in a classical linear group G. In this paper we find all simple rational G-modules V such that for each vector vV the closure of the T-orbit of v is a normal affine variety. For every G-module without this property we present a T-orbit with nonnormal closure. To solve this problem, we use a combinatorial criterion of normality which is formulated in terms of the set of weights of a simple G-module. The same problem for G = SL(n) was solved by the author earlier.

Keywords

toric variety normality irreducible representation classical root system weight decomposition 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsIndependent University of Moscow and Poncelet Laboratory (UMI 2615 of CNRS)MoscowRussia

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