𝐺(𝐹_{𝑞})-invariants in irreducible 𝐺(𝐹_{𝑞²})-modules

Lusztig, G.

doi:10.1090/S1088-4165-00-00114-X

$G(F_{q})$-invariants in irreducible $G(F_{q^{2}})$-modules
HTML articles powered by AMS MathViewer

by G. Lusztig

Represent. Theory 4 (2000), 446-465

DOI: https://doi.org/10.1090/S1088-4165-00-00114-X

Published electronically: September 14, 2000

PDF | Request permission

Abstract:

We give an explicit formula for the dimension of the space of $G(F_{q})$-invariant vectors in an irreducible complex representation of $G(F_{q^{2}})$, where $G$ is a connected reductive algebraic group defined over a finite field $F_{q}$ with connected center.

References

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

Über die reellen Darstellungen der endlichen Gruppen

Roderick Gow, Two multiplicity-free permutation representations of the general linear group $\textrm {GL}(n,q^2)$, Math. Z. 188 (1984), no. 1, 45–54. MR 767361, DOI 10.1007/BF01163871
Noriaki Kawanaka, On subfield symmetric spaces over a finite field, Osaka J. Math. 28 (1991), no. 4, 759–791. MR 1152953
George Lusztig, Characters of reductive groups over a finite field, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR 742472, DOI 10.1515/9781400881772
Radu Bǎdescu, On a problem of Goursat, Gaz. Mat. 44 (1939), 571–577. MR 0000087, DOI 10.1016/0001-8708(86)90071-X
George Lusztig, On the character values of finite Chevalley groups at unipotent elements, J. Algebra 104 (1986), no. 1, 146–194. MR 865898, DOI 10.1016/0021-8693(86)90245-0
G. Lusztig, Leading coefficients of character values of Hecke algebras, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 235–262. MR 933415, DOI 10.1090/pspum/047.2/933415
George Lusztig, Symmetric spaces over a finite field, The Grothendieck Festschrift, Vol. III, Progr. Math., vol. 88, Birkhäuser Boston, Boston, MA, 1990, pp. 57–81. MR 1106911, DOI 10.1007/978-0-8176-4576-2_{3}
George Lusztig, Green functions and character sheaves, Ann. of Math. (2) 131 (1990), no. 2, 355–408. MR 1043271, DOI 10.2307/1971496
P. Erdös, On the distribution of normal point groups, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 294–297. MR 2000, DOI 10.1073/pnas.26.4.294
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