Support Varieties of Non-Restricted Modules over Lie Algebras of Reductive Groups |
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Authors: | Premet Alexander |
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Institution: | Department of Mathematics, University of Manchester Oxford Road, Manchester M13 9PL. E-mail: sashap{at}ma.man.ac.uk |
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Abstract: | Let G be a connected semisimple group over an algebraicallyclosed field K of characteristic p>0, and g=Lie (G). Fixa linear function g* and let Zg() denote the stabilizer of in g. Set Np(g)={xg|xp]=0}. Let C(g) denote the category offinite-dimensional g-modules with p-character . In 7], Friedlanderand Parshall attached to each MOb(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, p2if G has a component of type Bn, Cn or F4, and p3 if G has acomponent of type G2. It is proved in this paper that, for anynonzero MOb(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]. |
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