Strong indecomposability conjecture for Bernstein components of Zelevinsky restrictions

Let $\mathfrak m$ be a multisegment for $n+1$, and let $\zeta(\mathfrak m)$ denote the associated Zelevinsky induced module. For the restriction to $G_n$, a Bernstein component is the corresponding Bernstein-isotypic component, and a module is strongly indecomposable when it has the property specified by the paper's definition. Strong indecomposability conjecture. Any Bernstein component of

$$\zeta(\mathfrak m)|_{G_n}$$

is strongly indecomposable. This is presented as a stronger statement of the paper's theorem on irreducible indecomposability; the conjecture concerns the structure of every Bernstein component of the restricted Zelevinsky induced module.