Speaker: Nancy Scherich

 

Tittle: What the Hecke?

 

Abstract: Maybe you have heard the phrase "the Burau representation is unitary". Well as it turns out, there are lots of representations of the braid group that also have this "unitary" property. In this talk, I will describe how to get representations of the braid groups using the Hecke algebras and Young tableaux. Darren and I have strong suspicion (and almost a proof!) that all of the representations that arise in this way are "unitary". I will discuss our progress so far and our evidence for why this is true. There are several pieces to this puzzle that I don't quite understand, but I will try to give you as complete a picture as I can.