Abstract
This is a review of an object oriented computer algebra system which is devoted to epresentation theory, invariant theory and combinatorics of the symmetric group. Moreover, it can be used for classical multivariate polynomials via the different actions of the symmetric group on the algebra of polynomials. The review contains a brief introduction to the basic methods used. Schubert polynomials are introduced, examples are given, and some applications are described. In particular, they provide a new algorithm for the evaluation of Littlewood-Richardson coefficients via symbolic computations using integer sequences instead of partitions, tableaux or lattice permutations.
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