AN ALGORITHM TO COMPUTE BASES AND REPRESENTATION-MATRICES FOR SLN-REPRESENTATIONS(1)

We construct a basis for irreducible representations of the complex Li e 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 add ition we provide a straightening law which can be used to define an al gorithm to compute the representation matrix of elements of sL(n+1) wi th respect to this basis. The method can be generalized to all complex simple Lie algebras with a simply laced root system. (C) 1997 Elsevie r Science B.V.