I’ve written a series of posts about representation theory on my other site:

- Representation Theory – Basic Definitions
- Direct Sums and Tensor Products
- Irreducible and Indecomposable Representations
- Decomposing Representations
- The Group Ring and the Regular Representation

The emphasis is on illustrating all the above things in Sage. It’s pretty elementary, and uses linear algebra more than anything else. I haven’t touched character theory yet; that will be covered in the next series of posts.