The co-Pieri rule for Kronecker coefficients

Abstract

A fundamental problem in the representation theory of the symmetric group, Sn, is to describe the coefficients in the decomposition of a tensor product of two simple representations. These coefficients are known in the literature as the Kronecker coefficients. The Littlewood--Richardson coefficients appear as an important subfamily of the wider class of stable Kronecker coefficients. This subfamily of coefficients can be calculated using a tableaux counting algorithm known as the Littlewood--Richardson rule. This paper generalises one half of this rule (the "co-Pieri" rule) to the the wider family of stable Kronecker coefficients.