# What are the elements of the antisymmetric representation of $SU(4)$ in a matrix form?

I would like to know the $4\times 4$ matrices that correspond to the antisymmetric representation of $SU(4)$. I know that there should be a relation with a $6$ representation of $SO(6)$. Is there a way to obtain a matrix representation of these antisymmetric rep of $SU(4)$. Where do I start?

• By the antisymmetric rep do you mean $SU(4)$ acting on $\Lambda^2\Bbb C^4$? Are you asking how to turn matrices in $SU(4)$ into matrices in $GL(6,\Bbb C)$, or what are you asking? – anon Dec 23 '17 at 20:26

I'm pretty convinced you misunderstood the 4×4 bit. You wanted to say ${\mathbf 4} \otimes_A {\mathbf 4} ={\mathbf 6}$, so the antisymmetrized Kronecker product of two fundamental reps of su(4), the one whose Young tableau is two boxes stacked on top of each other. (For su(3) this would have been the $\bar{\mathbf 3}$, the antiquark.)