Partitions of n index both the Jordan canonical forms of
nilpotent nxn matrices, and the irreducible representations of $S_n$.
I'll explain how to construct the second from the first.
One upshot will be that the representations come with natural bases
(over the integers, even with some predictable signs).
I'll hint about how this generalizes to all representations of all
compact connected Lie (not finite) groups, and talk about some
open research directions.

Zoom Info: https://cornell.zoom.us/j/98575181908?pwd=TnM0YXNnSHg3WnA5Ym9Pc1lZUnpjUT09

Meeting ID: 985 7518 1908
Passcode: 1h934d