Irreducible Harish-Chandra modules over G with nontrivial A_n' action are either cuspidal or generalized highest weight modules, and the latter reduce to ordinary highest weight modules for a suitable triangular decomposition, yielding a full classification.
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Classification of irreducible Harish-Chandra modules over extended Divergence-zero Lie algebras
Irreducible Harish-Chandra modules over G with nontrivial A_n' action are either cuspidal or generalized highest weight modules, and the latter reduce to ordinary highest weight modules for a suitable triangular decomposition, yielding a full classification.