Simple SL(n)-Modules with Normal Closures of Maximal Torus Orbits

2008/06/12 by Karine Kuyumzhiyan, K. Kuyumzhiyan, Kuyumzhiyan, K.
Mathematics · #Advanced Differential Equations and Dynamical Systems #math.AG #math.CO #msc:05E15 #msc:14M25 #msc:14R20

paper · pdf · doi:10.48550/arxiv.0806.1981

arxiv created 2008/06/12 · arxiv updated 2009/12/01

Abstract

Let T be the subgroup of diagonal matrices in the group SL(n). The aim of this paper is to find all finite-dimensional simple rational SL(n)-modules V with the following property: for each point v∈ V the closure Tv of its T-orbit is a normal affine variety. Moreover, for any SL(n)-module without this property a T-orbit with non-normal closure is constructed. The proof is purely combinatorial: it deals with the set of weights of simple SL(n)-modules. The saturation property is checked for each subset in the set of weights.

Related

• Simple Modules of Classical Linear Groups with Normal Closures of Maximal Torus Orbits
• Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits
• Admissible modules and normality of classical nilpotent orbits I
• Affine toric varieties with an open orbit of an SL_n action
• Normality of orbit closures for directing modules over tame algebras