### Young Diagrams and Schur Functors

#### Posted by John Baez

What would you do if someone told you to invent something a lot like the natural numbers, but even cooler? A tough challenge!

I’d recommend ‘Young diagrams’.

I gave a talk about Young diagrams yesterday at Math Connections — a conference organized by grad students here at U.C. Riverside. Check out my talk here:

Young diagrams are fundamental in group representation theory because they give ‘Schur functors’ — ways to turn one group representation into another, which apply in a completely general way to *any* representation.

Todd Trimble and I figured out a new way to think about this, which I explained briefly in my talk. Joe Moeller took notes and I polished them up a bit.

## Re: Young Diagrams and Schur Functors

Like the natural numbers, but cooler … my first thought would be PROPs, as expounded here and at https://graphicallinearalgebra.net (sorry; I don’t know how to make that a clickable link). On the other hand, as a representation theorist, I’m happy about anything that leads to representation theory. Is there any way to see PROPs as a special case of Young diagram?