I've been looking at Paul Langacker's "Grand unified theories and proton decay" for a course on GUTs. I'm stuck with the 16 irrep of SO(10), particularly I don't understand how to prove the statement that the 16 decomposes as 5* + 10 + 1. I can see why it's useful physics wise, but I would like to understand where it comes from mathematics wise. My lack of a decent group theory basics knowledge doesn't really help here.
Continuing from that if you look at 16 x 16 to get to a 126 for a Maiorana mass term, it would be my first idea to use Young tableaux and do it like I've done 5x5, 5x10 etc. in SU(5). However, I don't know what the young tableau of a 16 would be in SO(10). Maybe that would get me started?
Thanks for help towards a solution, or any decent references where I can look.
The Attempt at a Solution
- I don't know how to do decompositions
- I tried working with Young tableaux, but with 16 that's a problem for me