Let $F$ be a nonarchimedean local field and $G$ the $F$-points of a connected simply connected reductive group over $F$. We study the unipotent $\ell$-blocks of $G$, for $\ell \ne p$. 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.

让$F$是一个非阿基米德局部场并且$G$这$F$- 连接的简单连接的还原基团的点$F$。我们研究单能$\ell$- 块$G$， 为了$\ell \ne p$。为此，我们引入以下概念：$（d,1）$- 有限还原群的级数。这些级数形成了不可约表示的划分，并使用 Harish-Chandra 理论和定义$d$-哈里什-钱德拉理论。这$\ell$-然后使用这些构建块$（d,1）$-系列，与$d$的顺序$q$模数$\ell$，以及 Bruhat-Tits 构建上的一致幂等系统$G$。我们还描述了稳定的$\ell$-无分支经典群的深度零范畴的分块分解。