# Representations of SU(3) Algebra

1. Dec 10, 2015

### dman12

1. The problem statement, all variables and given/known data

I'm trying to figure out this question:

"Show that the 10-dimensional representation R3,0 of A2 corresponds to a reducible representation of the LC[SU(2)] subalgebra corresponding to any root. Find the irreducible components of this representation. Does the answer depend on the particular root chosen?"

2. Relevant equations

3. The attempt at a solution

So I am happy finding the decuplet of A2, which is just complexified L[SU(3)]. You get a triangle of the 10 weights, which are two dimensional due to the fact that the Lie algebra is rank 2.

But I don't get how you can view this as being a reducible representation of complexified L[SU(2)]. The weights of L[SU(2)] representations are one dimensional so how can we build a two dimensional weight system from them?

2. Dec 15, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?