Summer REU 2026 - Categorical representation theory

Project summary

Last summer we saw how most of the basic structures of representation theory can be re-contextualized in the setting of category theory. However, one of the biggest tools of classical representation theory is character theory and we haven't yet seen a categorical interpretation for characters. As such, our immediate aims are to:

1. Find a categorical interpretation of characters.
2. Find a categorical interpretation/method of performing "calculations" in representation theory; e.g., computing character tables, inner products, etc.
3. Look for purely categorical proofs of classical results involving characters.

Meeting notes

Task list

Tasks will be added after each meeting.

Classical character theory

• Read Section 18.3 in Dummit & Foote and check out the following exercises:
  • Exercise 1
  • Exercise 2
  • Exercise 5
  • Exercise 6
  • Exercise 7
  • Exercise 8
  • Exercise 11
  • Exercise 12
  • Exercise 13

The team

Mark Muzquiz

mamuzqui@calpoly.edu

References

Dummit & Foote, Abstract Algebra (Chapters 18 and 19)
Mac Lane, Categories for the Working Mathematician