# 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?