Defining relations are relations among the generators of a group, $\{g_a\}$, such that $\prod g_a^{n_a}=e$, where $e$ is the identity element. The multiplication rule of a group can always be specified by a set of defining relations.
For $SU(2)$ and $SU(4)$, what are the sets of defining relations that completely specify their multiplication rules? Do they depend on the representations?