The generic-extension subrepresentation conjecture of Lapid and Mínguez

Let $C,D\in\mathbf{Comp}$, and let $C*D$ denote the generic extension of the two components. Let $\pi(C)$ be the irreducible representation corresponding to $C$.

Generic-extension subrepresentation conjecture. The representation $\pi(C*D)$ is a subrepresentation of

$$\pi(C)\times\pi(D).$$

The conjecture concerns the relationship between the generic-extension operation on irreducible components and parabolic induction. It is stated in the source as a conjecture of Lapid and Mínguez; its resolution is not given in the supplied text.