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Homework Help: Transformation of the adjoint representation

  1. Jan 23, 2010 #1
    1. The problem statement, all variables and given/known data
    given that

    [tex]N\otimes\bar{N} = 1 \oplus A [/tex]

    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 [itex] 2 \oplus (N-2) [/itex]

    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 [tex] T^a [/tex]

    that it transfors as [tex] T^a \rightarrow \sigma \, \lambda \, T^a [/tex]

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