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• W2247762725 abstract "Let G be a simply connected simple algebraic group over an algebraically closed field K of characteristic p>0 with root system R, and let ${mathfrak g}={cal L}(G)$ be its restricted Lie algebra. Let V be a finite dimensional ${mathfrak g}$-module over K. For any point $vinV$, the {it isotropy subalgebra} of $v$ in $mathfrak g$ is ${mathfrak g}_v={xin{mathfrak g}/xcdot v=0}$. A restricted ${mathfrak g}$-module V is called exceptional if for each $vin V$ the isotropy subalgebra ${mathfrak g}_v$ contains a non-central element (that is, ${mathfrak g}_vnotsubseteq {mathfrak z(mathfrak g)}$). This work is devoted to classifying irreducible exceptional $mathfrak g$-modules. A necessary condition for a $mathfrak g$-module to be exceptional is found and a complete classification of modules over groups of exceptional type is obtained. For modules over groups of classical type, the general problem is reduced to a short list of unclassified modules. The classification of exceptional modules is expected to have applications in modular invariant theory and in classifying modular simple Lie superalgebras." @default.
• W2247762725 created "2016-06-24" @default.
• W2247762725 creator A5062322061 @default.
• W2247762725 date "2014-11-19" @default.
• W2247762725 modified "2023-09-24" @default.
• W2247762725 title "Exceptional representations of simple algebraic groups: in prime characteristic" @default.
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• W2247762725 hasPublicationYear "2014" @default.
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