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Dear gap-forum,I'm far to be an expert in representation theory and in GAP, but I'm

looking for a Chevalley module V for G=SO(4,C), taht is to say a faithful

finite dimensional SO(4,C)-module such that:

1. V contains no one-dimensional G-modules

2. any proper connected closed subgroup H $\in$ G leaves a one-dimensional

subspace W $\in$ V invariant.

I'd be interested in an injection of the representation of so(4,C) by the

set of matrices X such that tX.M+M.X=0, with M=[[0,I_2],[I_2,0]], in gl(V)

because I'm looking actually for the image of a regular pair of generators

of so(4,C) [which I know for the previous representation] in a Chevalley

module for SO(4,C).

Hoping it may interest some of you too,

Best regards,

Philippe Gaillard

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