Abstract
We construct a basis for irreducible representations of the complex Lie algebra sL n + 1 . The basis is obtained by applying certain monomials in the enveloping algebra of SL n + 1 to a highest weight vector. In addition we provide a straightening law which can be used to define an algorithm to compute the representation matrix of elements of sL n + 1 with respect to this basis. The method can be generalized to all complex simple Lie algebras with a simply laced root system.
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