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Let k[g] be the algebra of polynomial functions on g and let k[g]^G be the algebra of invariants under the conjugation action of G. For all weights chi in Z^n with chi_2<=0 or chi_{n-1}>=0 we give explicit bases for the k[g]^G-module k[g]^U_chi of highest weight vectors of weight chi. This extends earlier results to a much bigger class of weights. 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