论文标题
通过限制数据来限制超悬来表示
Restricting Supercuspidal Representations via a Restriction of Data
论文作者
论文摘要
令$ f $为剩余特征$ p $的非一切本非一切本。令$ \ mathbb {g} $为一个还原的$ f $定义的还原组，该组分裂在驯服的扩展程序上，并设置$ g = \ mathbb {g}（f）$。我们假设$ p $不划分$ \ mathbb {g} $的weyl ofter的顺序。给定一个封闭的连接的$ f $ -subGroup $ \ mathbb {h} $，其中包含$ \ mathbb {g} $的派生子组，我们研究了限制了不可减至的supercuspidal表示的$ h $ YU建设。我们通过限制数据限制了从$ψ$构造$ h $ data的数据，将$π| _h $的完整描述带入了不可约组件。类似地，我们定义了Kim-YU类型的限制，以研究对不是超级优势的$ g $不可还原表示的限制。
Let $F$ be a non-archimedean local field of residual characteristic $p$. Let $\mathbb{G}$ be a reductive group defined over $F$ which splits over a tamely ramified extension and set $G=\mathbb{G}(F)$. We assume that $p$ does not divide the order of the Weyl group of $\mathbb{G}$. Given a closed connected $F$-subgroup $\mathbb{H}$ that contains the derived subgroup of $\mathbb{G}$, we study the restriction to $H$ of an irreducible supercuspidal representation $π=π_G(Ψ)$ of $G$, where $Ψ$ is a $G$-datum as per the J.K. Yu Construction. We provide a full description of $π|_H$ into irreducible components, with multiplicity, via a restriction of data which constructs $H$-data from $Ψ$. Analogously, we define a restriction of Kim-Yu types to study the restriction of irreducible representations of $G$ which are not supercuspidal.
