Simple Modules of Classical Linear Groups with Normal Closures of Maximal Torus Orbits

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 v in V the closure of its T-orbit is a normal affine variety. For every other G-module we present a T-orbit with the non-normal closure. We use a combinatorial criterion of normality formulated in terms of the set of weights of a simple G-module. This work is a continuation of the previous work, where the same problem was solved in the case G=SL(n).