Group representations, interesting aspects?

[ArcanaNoir]

I am writing an undergraduate "thesis" on group representations (no original work, basically a glorified research paper). I was wondering if anyone could suggest interesting aspects that might be worth writing about in my paper.

I have only just begun to explore the topic, and I see that it is quite broad. I'm thinking I like finite groups, and maybe restricting the field over which I explore the matrices would be interesting. (besides, I'm not a fan of complex numbers..) I definitely plan to look into reductions and minimal representations. Sorry if my terminology is wrong, I'm really just beginning with this.

I'm really excited about this research, I love algebra!

Oh, and any books that you think might be helpful would be appreciated, especially books that are not very advanced. I haven't taken analysis or topology yet, and I'm finding a lot of material kind of inaccessible.

 

[micromass]

Good books would include "Algebra" from Artin and "Algebra" from Lang. They contain nice section on representation theory.

 

[ArcanaNoir]

thanks micro

 

[Stephen Tashi]

I find this blog interesting because he has a way of expressing the mathematical essence of ideas. (Although I also find the Wordpress blogs awkward to navigate. Google finds things in them better than the Wordpress interface.) http://drexel28.wordpress.com/2011/01/18/representation-theory-definitions-and-basics/

To me, the most interesting aspect of the representation of continuous groups is that the matrix entries (which are functions of the parameters that define the group) often turn out to be the important "special functions" of mathematical physics. This is only unified way that I know about for looking at the special functions.