Combinatorics Seminar: "A Diagram-Like Basis for the Multiset Partition Algebra"

Abstract: There’s a classical connection between the representation theory of the sym- metric group and the general linear group called Schur-Weyl Duality. Variations on this principle yield analogous connections between the symmetric group and other objects such as the partition algebra and more recently the multiset par- tition algebra. The partition algebra has a well-known basis indexed by graph- theoretic diagrams which allows the multiplication in the algebra to be under- stood visually as combinations of these diagrams. I will present an analogous basis for the multiset partition algebra and show how this basis can be used to construct representations for the algebra.

Host: Nathan Lesnevich