I am trying to show (to no avail),
$$ \int\limits_{U(N)} dU~U_{ij}U^{\dagger}_{kl} = \frac1N \delta_{il}\delta_{jk} $$
Where $dU$ is the normalized Haar measure on $U(N)$ and $U$ is a unitary matrix. I have never seen anything like this before and the literature I've found is a little over my head. Can these matrices be written in some other way to make sense of the integral or can we parameterize the group in some way? Any help is welcome.