On \bbf_q-rational structure of nilpotent orbits

2007/03/18 by Kaptanoglu, Semra, Parshall, Brian, Shu, Bin
#17B20 #17B35 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0703527

Abstract

Let G be a simple algebraic group and \ggg=\Lie(G) over k=\bbf_q where q is a power of the prime characteristic of k, and F a Frobenius morphism on G which can be defined naturally on \ggg. In this paper, we investigate the relation between F-stable restricted modules of \ggg and closed conical subvarieties defined over \bbf_q in the null cone \cn(\ggg) of \ggg. Furthermore, we clearly investigate the \bbf_q-rational structure for all nilpotent orbits in \ggg under the adjoint action of G when the characteristic of k is good for G and bigger than 3. The arguments are also valid when \ggg' is classical simple Lie algebra in the sense of \citeSel and G' is the adjoint group of \ggg'.

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