Cyclic representations of general linear p-adic groups

Let π1,…,πk be smooth irreducible representations of p-adic general linear groups. We prove that the parabolic induction product π1×⋯×πk has a unique quotient whose Langlands parameter is sum parameters all factors (cyclicity property), assuming same property holds for each products πi×πj (i<j), and but at most two πi×πi remains (square-irreducibility property). Our technique applies recently devised Kashiwara-Kim notion normal sequence modules quiver Hecke algebras. Thus, cyclicity problem reduced to recent Lapid-Mínguez conjectures on maximal case.