论文标题
单位$ \ ell $ -blocks简单连接$ p $ - adic groups
Unipotent $\ell$-blocks for simply-connected $p$-adic groups
论文作者
论文摘要
令$ f $为非一切本的非一切本和$ g $ $ f $ - $ f $ points的$ f $ f $ a $ f $。在本文中，我们研究了$ g $的Unipitent $ \ ell $ -Blocks，以$ \ ell \ neq p $。为此，我们介绍了有限还原组的$（D，1）$ - 系列的概念。这些系列构成了不可约表示的分区，并使用Harish-Chandra理论和$ d $ -Harish-Chandra理论定义。然后，使用这些$（D，1）$ - 系列构建$ \ ell $ -Blocks，并带有$ d $的订单$ q $ modulo $ \ ell $，以及在$ g $的Bruhat-tits建筑物上的一致型群体系统。我们还描述了一个未受到的古典群体的深度零类别的稳定$ \ ell $ -Block分解。
Let $F$ be a non-archimedean local field and $G$ the $F$-points of a connected simply-connected reductive group over $F$. In this paper, we study the unipotent $\ell$-blocks of $G$, for $\ell \neq p$. To that end, we introduce the notion of $(d,1)$-series for finite reductive groups. These series form a partition of the irreducible representations and are defined using Harish-Chandra theory and $d$-Harish-Chandra theory. The $\ell$-blocks are then constructed using these $(d,1)$-series, with $d$ the order of $q$ modulo $\ell$, and consistent systems of idempotents on the Bruhat-Tits building of $G$. We also describe the stable $\ell$-block decomposition of the depth zero category of an unramified classical group.
