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

AbstractWe construct a basis for irreducible representations of the complex Lie algebra sLn + 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 sLn + 1 with respect to this basis. The method can be generalized to all complex simple Lie algebras with a simply laced root system