Speaker: Tom Halverson, Macalester College

Title: Tensor Multiplicities for the Symmetric Group, Set Partitions, and Partition Algebras

Abstract: We will examine the multiplicity of irreducible symmetric group modules in the tensor product of its permutation module and its reflection module. These can be counted using vacillating tableaux and set partition tableaux. The projections onto these modules live in a quotient of the partition algebra. We describe the kernel of the partition algebra and multiplication in the image. This can be viewed as a partition algebra version of the fundamental theorems of invariant theory for the symmetric group.