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SO(N) adjoint rep. under SO(3) subgroup

  1. Oct 13, 2014 #1

    I'm having trouble figuring out how SO(N) adjoint rep. transforms

    under a SO(3) subgroup.

    Unlike SU(N), SO(N) fundamental N gives

    \begin{equation} N \otimes N = 1 \oplus A \oplus S \end{equation}

    So the \begin{equation} S \end{equation} part really bothers.

    Can you give a help?
    Last edited: Oct 13, 2014
  2. jcsd
  3. Oct 14, 2014 #2


    User Avatar
    Gold Member

    What about using indexes for the vector spaces associated to the tensor products? Sometimes it helps to visualize the situation, specially now that you want to separate the symmetric and antisymmetric parts.
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