On induction of class functions

Lusztig, G.

doi:10.1090/ert/561

On induction of class functions
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by G. Lusztig

Represent. Theory 25 (2021), 412-421

DOI: https://doi.org/10.1090/ert/561

Published electronically: May 7, 2021

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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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