Abstract:Let $G$ be a connected reductive group defined over a finite field $\mathbf {F}_q$ and let $L$ be a Levi subgroup (defined over $\mathbf {F}_q$) of a parabolic subgroup $P$ of $G$. We define a linear map from class functions on $L(\mathbf {F}_q)$ to class functions on $G(\mathbf {F}_q)$. This map is independent of the choice of $P$. We show that for large $q$ this map coincides with the known cohomological induction (whose definition involves a choice of $P$).

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中文翻译：

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关于班级职能的归纳

摘要：让$ G $是在有限域$ \ mathbf {F} _q $上定义的连通归约组，并让$ L $是抛物子组$的Levi子组（在$ \ mathbf {F} _q $上定义） $ G $的P $。我们定义了从$ L（\ mathbf {F} _q）$上的类函数到$ G（\ mathbf {F} _q）$上的类函数的线性映射。该地图与$ P $的选择无关。我们表明，对于较大的$ q $，该图与已知的同调归纳（其定义涉及$ P $的选择）重合。

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