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
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.
I’ve written an in-browser Sage interact script that generates the subgroup lattice for all groups of size up to 32. Click the image to access it!
Lattice of subgroups of the Dicyclic Group of order 12
Here’s my second subgroup lattice post:
Subgroup Lattices with Sage – Coloring Vertices. It shows how to color a poset according to properties that you’d like to highlight.
At the bottom of that post, you’ll also find a nice interactive section where you can play around with various groups and their subgroups. It looks like this:
These posts are pretty time-consuming to write, so the next post might be quite a while later. Have fun playing with the interactive subgroup demo!
Lattice of subgroups of the Dihedral Group of order 8.
I’ve started a new blog for demonstrating Sage code that can be run directly in the browser. I might write about that process later.
For now, here’s the first of a series of posts about creating and experimenting with the lattice of subgroups in Sage:
Lattice of Subgroups in Sage.
while Ivana watches “
My Love from the Star“… “The” star? Which star?
This list of links is mainly for my future reading. It’s roughly a list of future research directions that I might want to consider.
Background for a friend’s photoshoot. She’s a number theorist. Incidentally, her birthday is on Dec 13, and 1213 is a prime.