Universal irreducibility structure for Harish-Chandra parabolic induction

Let $G$ be a reductive group, let $P=MN$ be a parabolic subgroup, and let $I^G_P(\sigma)$ be the parabolic induction of an irreducible admissible representation $\sigma$ of $M$. Suppose that the reducibility conditions of $I^G_P(\sigma)$ lie in a standard Levi subgroup $L$ of a parabolic subgroup $Q=LV\subset P=MN$. For a representation $\tau$ in the Jordan–Hölder set $JH(I^L_{L\cap P}(\sigma))$, write $I^G_Q(\tau)$ for the corresponding induced representation. Universal irreducibility conjecture. The representation $I^G_Q(\tau)$ is always irreducible for every $\tau\in JH(I^L_{L\cap P}(\sigma))$. This conjecture proposes a universal hierarchical structure for reducibility: once all reducibility conditions are contained in the smaller Levi subgroup $L$, induction from $Q$ to $G$ should introduce no further reducibility. The paper presents this as a conjectural direction motivated by a Muller-type irreducibility criterion; no resolution is supplied.