## On induction of class functions

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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 $P$).## References

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## Additional Information

**G. Lusztig**- Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Email: gyuri@mit.edu
- 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
- © Copyright 2021 American Mathematical Society
- Journal: Represent. Theory
**25**(2021), 412-421 - MSC (2020): Primary 20G99
- DOI: https://doi.org/10.1090/ert/561
- MathSciNet review: 4263412