C&O Master's Thesis Presentation - Cameron Marcott

Title: The representation theory of the partition algebra and the 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 algebra on tensor space. An analysis of the representation theory of the partition results elucidates the relationship between the Kronecker coefficients and the reduced Kronecker coefficients.