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Representation Theory

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On induction of class functions

Author: G. Lusztig
Journal: Represent. Theory 25 (2021), 412-421
MSC (2020): Primary 20G99
Published electronically: May 7, 2021
MathSciNet review: 4263412
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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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Additional Information

G. Lusztig
Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
MR Author ID: 117100

Received by editor(s): July 31, 2020
Received by editor(s) in revised form: November 27, 2020, and December 4, 2020
Published electronically: May 7, 2021
Additional Notes: This research was supported by NSF grant DMS-1855773
Article copyright: © Copyright 2021 American Mathematical Society