论文标题
在一般线性组的内部形式的产品函子上，非一切本局部字段
On the product functor on inner forms of the general linear group over a non-Archimedean local field
论文作者
论文摘要
令$ g_n $为非架构字段上一般线性组的内部形式。我们修复了$ g_n $的任意不可约的表示$σ$。当诱导数据是$π\ boxtimesσ$时，lapid-mínguez给出了抛物线诱导不可减至的组合标准。我们表明，它们的标准可用于定义一些$ g_m $的平滑表示类别的完整子类别，在该类别上，抛物线电感函数$τ\ mapstoτ\ timesσ$完全fallaithful。我们对完全信仰的证明的关键要素是长度2的不可分解表示的构建。 以前已应用于特殊情况的这种结果在证明非一切型非固定属性一般线性群体的局部非脾气的gan-gross-prosad猜想中。在本文中，我们采用完全信仰的结果来证明由jacquet functor引起的某种大衍生物满足其Socle是不可还原的特性，并且在大衍生产品的Jordan-Hölder序列中具有多重性。
Let $G_n$ be an inner form of a general linear group over a non-Archimedean field. We fix an arbitrary irreducible representation $σ$ of $G_n$. Lapid-Mínguez give a combinatorial criteria for the irreducibility of parabolic induction when the inducing data is of the form $π\boxtimes σ$ when $π$ is a segment representation. We show that their criteria can be used to define a full subcategory of the category of smooth representation of some $G_m$, on which the parabolic induction functor $τ\mapsto τ\times σ$ is fully-faithful. A key ingredient of our proof for the fully-faithfulness is constructions of indecomposable representations of length 2. Such result for a special situation has been previously applied in proving the local non-tempered Gan-Gross-Prasad conjecture for non-Archimedean general linear groups. In this article, we apply the fully-faithful result to prove a certain big derivative arising from Jacquet functor satisfies the property that its socle is irreducible and has multiplicity one in the Jordan-Hölder sequence of the big derivative.
