Abstract: I briefly explore the mathematical concept of duality and
how it is fundamental in our algebraic thinking. Then I survey one
particular instance of duality in the character theory of finite
groups: the relation of irreducible characters and conjugacy classes.
This viewpoint of duality gives us a way to turn results upside down,
I will show examples of this.
Then I describe one potential way to extend this kind of duality to a
structurally stronger one and how this project is limited. The talk
will be based on two papers:
Andrus, Ivan; Hegedüs Pál: Determination of conjugacy class sizes from
products of characters, Archiv der Mathematik (Basel) 100 no.1.
Andrus, Ivan; Hegedüs Pál; Okuyama, Tetsuro: Transposable Character
Tables, Dual Groups, Math Proc Cambridge Phil Soc 157 no 1. (2014)
You can watch this lecture here: