Multivariate polynomials, standard tableaux, and representations of symmetric groups

This paper is concerned with structural and algorithmic aspects of certain R-bases in polynomial rings R[X_ij] over a commutative ring R with 1. These bases are related to standard tableaux. We shall examine the main tools in full detail: (symmetrized) bideterminants, Capelli operators, hyperdominance, and generalized Laplace's expansions. These tools are then applied to the representation theory of symmetric groups. In particular, we present an algorithm which efficiently computes for every skew module of a symmetric group an R-basis which is adapted to a Specht series. This result is a constructive, characteristic-free analogue of the celebrated Littlewood-Richardson rule. This paper will serve as the basis for a possible generalization of that rule to more general shapes.