# Does anyone know how to symmetrize $\gamma$-matrices?

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?

• Which $6_S + 4_A$ representation? – Qmechanic Mar 30 at 8:30
• 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"? – Super stuff Mar 30 at 8:50