Partition Algebras and Kronecker Coefficients

Abstract

Classical Schur-Weyl duality relates the representation theory of the general linear group to the representation theory of the symmetric group via their commuting actions on tensor space. With the goal of studying Kronecker products of symmetric group representations, the partition algebra is introduced as the commutator algebra of the diagonal action of the symmetric group on tensor space. An analysis of the representation theory of the partition offers results relating reduced Kronecker coefficients to Kronecker coefficients.