An algorithm to compute bases and representation matrices for SLn+1-representations

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 SLn+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. (C) 1997 Elsevier Science B.V.