** 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.