On the Kronecker Product s(n-p,p) * sλ

The Kronecker product of two Schur functions s λ and s µ , denoted s λ * s µ , is defined as the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group indexed by partitions of n, λ and µ, respectively. The coefficient, g λ,µ,ν , of s ν in s λ * s µ is equal to the multiplicity of the irreducible representation indexed by ν in the tensor product. In this paper we give an algorithm for expanding the Kronecker product s (n−p,p) * s λ if λ 1 − λ 2 ≥ 2p. As a consequence of this algorithm we obtain a formula for g (n−p,p),λ,ν in terms of the Littlewood-Richardson coefficients which does not involve cancellations. Another consequence of our algorithm is that if λ 1 − λ 2 ≥ 2p then every Kronecker coefficient in s (n−p,p) * s λ is independent of n, in other words, g (n−p,p),λ,ν is stable for all ν.