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I'm trying to construct the SO(5, 5) $\gamma$-matrices which are real and symmetric. Recently, I have 6 symmetric and 4 antisymmetric $\gamma$-matrices ($6_S + 4_A$ representation). How can I transform (or symmetrize) them to $10_S + 0_A$ representation?

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  • $\begingroup$ Which $6_S + 4_A$ representation? $\endgroup$ – Qmechanic Mar 30 at 8:30
  • $\begingroup$ SO(5,5) gammas are 32*32, right? Since I use Majorana-Weyl spinors, I can reduce the matrices to 16*16. Thus, here I only talk about 16*16 gammas (all real but 6 symmetric and 4 antisymmetric). Does it make sense? If not what do you mean by "which rep"? $\endgroup$ – Super stuff Mar 30 at 8:50

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