Kronecker multiplicities in the (k, ℓ) hook are polynomially bounded

Abstract

The problem of decomposing the Kronecker product of Sn characters is one of the last major open problems in the ordinary representation theory of the symmetric group Sn. In this note λ and µ are partitions of n, n goes to infinity, and we prove upper and lower polynomial bounds for the multiplicities of the Kronecker product χλ ⊗ χµ, where for some fixed k and l both partitions λ and µ are in the (k, l) hook.