论文标题
一般线性P-ADIC组的环状表示
Cyclic representations of general linear p-adic groups
论文作者
论文摘要
令$π_1，\ ldots，π_k$是$ p $ - adiC通用线性组的平滑表示。我们证明，抛物性诱导产品$π_1\ times \ cdots \ timesπ_k$具有独特的不可减至的商，其langlands参数是所有因素（环状属性）的参数的总和，假设每个产品的属性都具有$π_i\π_i\π_i\最终的两次$ i <j $ y <j $ y <j $ y <j $ y <j $ y < π_i$仍然是不可约的（平方迹法性属性）。我们的技术应用了Quiver Hecke代数的正常模块序列的最近设计的Kashiwara-Kim概念。 因此，将一般的环状问题降低到最近对最大抛物面情况的Lapid-Mínguez的猜想。
Let $π_1,\ldots,π_k$ be smooth irreducible representations of $p$-adic general linear groups. We prove that the parabolic induction product $π_1\times\cdots\times π_k$ 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 $π_i\times π_j$ ($i<j$), and that for all but at most two representations $π_i\times π_i$ 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.
