Linear maps preserving invariants

2007/08/21 by Gerald W. Schwarz, Schwarz, Gerald W.
Mathematics · #20G20 #22E46 #22E60 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20G20 #msc:22E46 #msc:22E60

paper · pdf · doi:10.48550/arxiv.0708.2890

minor changes

arxiv created 2007/11/13 · arxiv updated 2009/12/01

Abstract

Let G⊂\GL(V) be a complex reductive group. Let G' denote \ϕ∈\GL(V)| p∘ϕ=pfor all p∈\C[V]^G\. We show that, in general, G'=G. In case G is the adjoint group of a simple Lie algebra \lieg, we show that G' is an order 2 extension of G. We also calculate G' for all representations of \SL₂.

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