Representation Theory in Sage

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

  1. Representation Theory – Basic Definitions
  2. Direct Sums and Tensor Products
  3. Irreducible and Indecomposable Representations
  4. Decomposing Representations
  5. 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.

Holiday Harmonograph

harmonograph_loop

(Click picture for an online harmonograph generator)

When it’s snowing outside (or maybe not),

And your feet are cold (or maybe hot),

When it’s dark as day (or bright as night),

And your heart is heavy (and head is light),

What should you do (what should you say)

To make it all right (to make it okay)?

.

Just pick up a pen (a pencil will do),

Set up a swing (or three, or two),

And while the world spins (or comes to a still),

In your own little room (or on top of a hill),

Let your pendulum sway (in its time, in its way),

And watch as the pen draws your worries away!

Subgroup Lattices II – Coloring Vertices

Lattice of subgroups of the Dicyclic Group of order 12
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:

interact_demo

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!