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Here is a pattern of group embedding, $$ SU(4) \supset SU(3) \times U(1) $$ such that the irrep of SU(4) can be decomposed as the sum of tensor product of irrep of SU(3) and irrep of U(1).

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Two questions:

  • I wonder what will be the embedding for SO(6), $$ SO(6) \supset SU(2) \times G, $$ where, such that the irrep of SO(6) can be decomposed as the sum of tensor product of irrep of SU(2) and irrep of $G$?

  • alternatively what will be the embedding for $Spin(6)\simeq SU(4)$, $$ Spin(6)\simeq SU(4) \supset SU(2) \times G', $$ where, such that the irrep of SU(4) can be decomposed as the sum of tensor product of irrep of SU(2) and irrep of $G'$?

I only ask the proper ways to write the group $G$ and $G'$ here.

Here $G$ and $G'$ may be a product of several groups.

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  • $\begingroup$ you want to find all the possible $G$ and $G'$ on the right hand sides? $\endgroup$ – wonderich Oct 1 '18 at 4:57
  • $\begingroup$ yes! please help $\endgroup$ – annie heart Oct 1 '18 at 4:58

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