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

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

2008-06-12

arxiv.org/abs/0806.1981v1

Mathematics

Algebraic Geometry

Scientific paper

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 $v\in V$ the closure $\bar{Tv}$ 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.

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