Abstract
Complete bases are constructed for all finite-dimensional irreducible representations of the simple Lie algebras over C of the types An (n≥1), Bn and Cn (2≤n≤6), Dn (4≤n≤6), and G2. Each basis vector is given as an explicit sequence of weight-lowering generators of the algebra acting on the highest weight vector of the representation space. A similar construction (due to D-N. Verma) for the highest weight representations of all Kac–Moody algebras of rank 2 is presented as well.
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