Simple <Emphasis Type="Italic">SL</Emphasis>(<Emphasis Type="Italic">n</Emphasis>)-modules with normal closures of maximal torus orbits |
| |
Authors: | Karine Kuyumzhiyan |
| |
Institution: | 1.Department of Higher Algebra, Faculty of Mechanics and Mathematics,Moscow State University,Moscow,Russia |
| |
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)]\overline{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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|