Support Varieties of Non-Restricted Modules over Lie Algebras of Reductive Groups |
| |
Authors: | Premet Alexander |
| |
Institution: | Department of Mathematics, University of Manchester Oxford Road, Manchester M13 9PL. E-mail: sashap{at}ma.man.ac.uk |
| |
Abstract: | Let G be a connected semisimple group over an algebraicallyclosed field K of characteristic p>0, and g=Lie (G). Fixa linear function ![{chi}](http://jlms.oxfordjournals.org/math/chi.gif) g* and let Zg( ) denote the stabilizer of in g. Set Np(g)={x g|xp]=0}. Let C (g) denote the category offinite-dimensional g-modules with p-character . In 7], Friedlanderand Parshall attached to each M Ob(C (g)) a Zariski closed, conicalsubset Vg(M) Np(g) called the support variety of M. Suppose thatG is simply connected and p is not special for G, that is, p 2if G has a component of type Bn, Cn or F4, and p 3 if G has acomponent of type G2. It is proved in this paper that, for anynonzero M Ob(C (g)), the support variety Vg(M) is contained inNp(g) Zg( ). This allows one to simplify the proof of the KacWeisfeilerconjecture given in 18]. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|