Does there exist a computer algebra system that can work with finite-dimensional complex representations of the symmetric groups on finitely many letters? It should have the following functionality: (1) a way to produce all the irreps (e.g. via Specht modules) (2) irreps should come with a preferred choice of basis and there should be a function mapping a given permutation to the corresponding matrix (3) a way to take tensor products, direct sums, symmetric and exterior powers (4) a function giving the decomposition into irreps for an arbitrary finite-dimensional complex representation.
SageMath does have (1) and (2) but not (3) as far as I know. It probably is possible to do everything except (2) in some combinatorics packages but (2) is essential here.