Journal of Algebra ( IF 0.8 ) Pub Date : 2021-06-07 , DOI: 10.1016/j.jalgebra.2021.05.013 Maxim Gurevich , Alberto Mínguez
Let be smooth irreducible representations of p-adic general linear groups. We prove that the parabolic induction product 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 (), and that for all but at most two representations 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.
中文翻译:
一般线性p- adic群的循环表示
让 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 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 (),并且对于除最多两个表示之外的所有表示 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。