Cyclic representations of general linear p-adic groups

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