## Geometry & Representation - Mike Zabrocki (York University)

### Wednesday, March 28th, 2018

**Time:** 3:30 p.m. **Place:** Jeffery Hall 319

**Speaker:** Mike Zabrocki (York University)

**Title:** A Multiset Partition Algebra

**Abstract: ** Schur-Weyl duality is a statement about the relationship between the actions of the general linear group $Gl_n$ and the symmetric group $S_k$ when these groups act on $V_n^{\otimes k}$ (here $V_n$ is an $n$ dimensional vector space). If we consider the symmetric group $S_n$ as permutation matrices embedded in $Gl_n$, then the partition algebra $P_k(n)$ (introduced by Martin in the 1990's) is the algebra which commutes with the action of $S_n$.

In this talk I will explain how an investigation of characters of the symmetric group leads us to consider analogues of the RSK algorithm involving multiset tableaux. To explain the relationship of the combinatorics to representation theory we were led to the multiset partition algebra as an analogue of the partition algebra and the dimensions of the irreducible representations are the numbers of multiset tableaux.

This is joint work with Rosa Orellana of Dartmouth College.