On the Kronecker Product s(n-p,p) sλ

The Kronecker product of two Schur functions sλ and sμ, denoted sλ sμ, 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, gλ,μ,ν, of sν in sλ sμ 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) sλ if λ₁-λ₂≥ 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 λ₁-λ₂≥ 2p then every Kronecker coefficient in s(n-p,p) sλ is independent of n, in other words, g(n-p,p),λ,ν is stable for all ν.