Given non-zero $\xi \in \mathfrak{su}(n)$ and $G \in SU(n)$, consider the function:
$Q(U) = Tr(G^{\dagger}U)GU^{\dagger} - Tr(U^{\dagger}G) UG^{\dagger}$
(which just happens to be the gradient of $|Tr(UG^{\dagger})|^2$ right translated to the identity, and thus in $\mathfrak{su}(n)$).
What is $\max_{U} Tr(\xi^{\dagger}Q(U))$, and if possible the $U$ achieving this.
