Given a group $G$ and two Gelfand subgroups $H$ and $K$ of $G$, associated to an irreducible representation $\pi$ of $G$, there is a notion of $H$ and $K$ being correlated with respect to $\pi$ in $G$. This notion is defined by Benedict Gross in 1991. We discuss this theme and give some details in a specific example (which is joint work with Arindam Jana).