Sparse Interpolation of Symmetric Polynomials

Abstract

We develop efficient algorithms for computing the expansion of a given symmetric polynomial into Schur functions. This problem frequently arises in applications as the problem of decomposing a given representation of the symmetric (or general linear) group into irreducible constituents. Our algorithms are probabilistic, and run in time which is polynomial in the sizes of the input and output. They can be used to compute Littlewood–Richardson coefficients, Kostka numbers, and irreducible characters of the symmetric group.