Let ${\pi }_1,\dots ,{\pi }_k$ be smooth irreducible representations of p-adic general linear groups. We prove that the parabolic induction product ${\pi }_1\times \cdots \times {\pi }_k$ 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 ${\pi }_i\times {\pi }_j$ ($i<j$), and that for all but at most two representations ${\pi }_i\times {\pi }_i$ 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.

让 ${\pi }_1,\dots ,{\pi }_{克}$是p- adic 一般线性群的平滑不可约表示。我们证明抛物线归纳积${\pi }_1\times \cdots \times {\pi }_{克}$ 有一个唯一的不可约商，其朗兰兹参数是所有因子的参数之和（循环属性），假设每个产品都具有相同的属性 ${\pi }_{\mathrm{一世}}\times {\pi }_j$ ($\mathrm{一世}<j$)，并且对于除最多两个表示之外的所有表示 ${\pi }_{\mathrm{一世}}\times {\pi }_{\mathrm{一世}}$保持不可约（平方不可约属性）。我们的技术应用了最近设计的 Kashiwara-Kim 概念，即 quiver Hecke 代数的正常模块序列。

因此，一般的循环问题被简化为最近在最大抛物线情况下的 Lapid-Mínguez 猜想。