Construction of Weight Spaces for Irreducible Representations of An, Bn, Cn, Dn

Abstract

An algebraic technique is presented by means of which the weight space for the irreducible representations (λ) of An, Bn, Cn, Dn can be constructed from the weight spaces associated with the representations (λ′) of the subalgebras An−1, Bn−1, Cn−1, Dn−1. Since each chain ends with A1, all weight spaces of the classical simple Lie algebras associated with (λ) can be constructed, ultimately, from the well-known representations of A1.