# Transformation of the adjoint representation

1. Jan 23, 2010

### ansgar

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

$$N\otimes\bar{N} = 1 \oplus A$$

consinder the SU(2) subgroup of SU(N), that acts on the two first components of the fundamental representation N of SU(N). Under this SU(2) subgroup, the repsentation N of SU(N) transforms as $2 \oplus (N-2)$

with info above, how does the adjoint representation transform under this SU(2) subgroup?

3. The attempt at a solution

what does it mean that the representation transforms?

does it mean if I take one generator of the fundamental representation call it $$T^a$$

that it transfors as $$T^a \rightarrow \sigma \, \lambda \, T^a$$

where sigma is a SU(2) transformation matrix and lambda a SU(N-2) transf. matrix?