On induction of class functions

Lusztig, G.

doi:10.1090/ert/561

On induction of class functions
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Represent. Theory 25 (2021), 412-421 Request permission

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

Cédric Bonnafé and Jean Michel, Computational proof of the Mackey formula for $q>2$, J. Algebra 327 (2011), 506–526. MR 2746047, DOI 10.1016/j.jalgebra.2010.10.030
P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), no. 1, 103–161. MR 393266, DOI 10.2307/1971021
François Digne and Jean Michel, Representations of finite groups of Lie type, London Mathematical Society Student Texts, vol. 95, Cambridge University Press, Cambridge, 2020. Second edition of [ 1118841]. MR 4211777, DOI 10.1017/9781108673655
Meinolf Geck and Gunter Malle, The character theory of finite groups of Lie type, Cambridge Studies in Advanced Mathematics, vol. 187, Cambridge University Press, Cambridge, 2020. A guided tour. MR 4211779, DOI 10.1017/9781108779081
G. Lusztig, On the finiteness of the number of unipotent classes, Invent. Math. 34 (1976), no. 3, 201–213. MR 419635, DOI 10.1007/BF01403067
George Lusztig, Representations of finite Chevalley groups, CBMS Regional Conference Series in Mathematics, vol. 39, American Mathematical Society, Providence, R.I., 1978. Expository lectures from the CBMS Regional Conference held at Madison, Wis., August 8–12, 1977. MR 518617, DOI 10.1090/cbms/039
G. Lusztig, Intersection cohomology complexes on a reductive group, Invent. Math. 75 (1984), no. 2, 205–272. MR 732546, DOI 10.1007/BF01388564
George Lusztig, Character sheaves. II, III, Adv. in Math. 57 (1985), no. 3, 226–265, 266–315. MR 806210, DOI 10.1016/0001-8708(85)90064-7
George Lusztig, Character sheaves. V, Adv. in Math. 61 (1986), no. 2, 103–155. MR 849848, DOI 10.1016/0001-8708(86)90071-X
George Lusztig, Green functions and character sheaves, Ann. of Math. (2) 131 (1990), no. 2, 355–408. MR 1043271, DOI 10.2307/1971496
G. Lusztig, Character sheaves on disconnected groups. V, Represent. Theory 8 (2004), 346–376. MR 2077486, DOI 10.1090/S1088-4165-04-00251-1
G. Lusztig, On the cleanness of cuspidal character sheaves, Mosc. Math. J. 12 (2012), no. 3, 621–631, 669 (English, with English and Russian summaries). MR 3024826, DOI 10.17323/1609-4514-2012-12-3-621-631
Toshiaki Shoji, Character sheaves and almost characters of reductive groups. I, II, Adv. Math. 111 (1995), no. 2, 244–313, 314–354. MR 1318530, DOI 10.1006/aima.1995.1024