×

zbMATH — the first resource for mathematics

Rationality properties of unipotent representations. (English) Zbl 1141.20300
Summary: We describe those unipotent representations of a finite group of Lie type which are defined over the rational numbers.

MSC:
20C33 Representations of finite groups of Lie type
20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
PDF BibTeX Cite
Full Text: DOI
References:
[1] Beilinson, A.A.; Bernstein, J.; Deligne, P., Faisceaux pervers, Astérisque, 100, (1982) · Zbl 0536.14011
[2] Deligne, P.; Lusztig, G., Representations of reductive groups over finite fields, Ann. of math., 103, 103-161, (1976) · Zbl 0336.20029
[3] Geck, M.; Pfeiffer, G., Characters of finite Coxeter groups and iwahori – hecke algebras, (2000), Clarendon Press Oxford · Zbl 0996.20004
[4] Geck, M.; Kim, S.; Pfeiffer, G., Minimal length elements in twisted conjugacy classes of finite Coxeter groups, J. algebra, 229, 570-600, (2000) · Zbl 1042.20026
[5] Lusztig, G., Coxeter orbits and eigenspaces of Frobenius, Invent. math., 38, 101-159, (1976) · Zbl 0366.20031
[6] G. Lusztig, Lecture at the US-France Conference on Representation Theory, Paris, 1982, unpublished
[7] Lusztig, G., Characters of reductive groups over a finite field, Ann. of math. stud., 107, (1984), Princeton University Press
[8] Lusztig, G., Character sheaves, I, Adv. math., 56, 193-237, (1985) · Zbl 0586.20018
[9] Lusztig, G., Character sheaves, V, Adv. math., 61, 103-155, (1986) · Zbl 0602.20036
[10] Ohmori, Z., The Schur indices of the cuspidal unipotent characters of the finite unitary groups, Proc. Japan acad. ser. A math. sci., 72, 111-113, (1996) · Zbl 0860.20035
[11] Weil, A., Basic number theory, (1967), Springer-Verlag · Zbl 0176.33601
[12] Weyl, H., The classical groups, (1939), Princeton University Press · JFM 65.0058.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.