Matrix representation of generator of (projective) $Z_N\times Z_N$ subgroup of $PSU(N)$ in the fundamental representation

Question

It is known that the $Z_2\times Z_2$ subgroup of $PSU(2)=SO(3)$ is projective in the fundamental representation of $SU(2)$ with the matrix representation of generators as: \begin{eqnarray} v=-i\sigma_z;\\ w=-i\sigma_x, \end{eqnarray} where $\sigma_i$'s are Pauli matrix and the projectiveness is \begin{eqnarray} vw=-wv. \end{eqnarray} My question is how to generalize it to $SU(N)$. In other words, how to find two generators $V$ and $W$ in the fundamental representation of $SU(N)$ such that \begin{eqnarray} VW=\exp\left(i\frac{2\pi}{N}\right)WV;\\ V^N\&W^N\in\text{Center of }SU(N). \end{eqnarray}