Abstract
LetG be a reductive group over a finite fieldk of a characteristicp. Π:G k → AutU is an irreducible representation ofG in “a general position”. Springer formulated a conjecture about values of the character of Π on unipotent elements. This conjecture is proved in the article.
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References
P. Deligen,La conjecture de Weil, Publ. Math. I. H. E. S.43 (1974), 273–307.
P. Deligne and G. Lusztig,Representations of reductive groups over finite fields, Ann. of Math.103 (1976), 103–161.
Lecture Notes 340, Springer-Verlag, 1973, pp. 384–400.
SGA4, Lecture Notes, 269, 270, 305, Springer-Verlag, 1973.
T. A. Springer,Generalization of Green's polynomials, in Proc. Symp. in Pure Math., Vol. 21, Providence, 1971, pp. 149–154.
T. A. Springer,Trigonometrical sums, Green functions of finite groups and representations of Weyl groups, Preprint W19, University of Utrecht, 1976.
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Kazhdan, D. Proof of Springer’s hypothesis. Israel J. Math. 28, 272–286 (1977). https://doi.org/10.1007/BF02760635
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DOI: https://doi.org/10.1007/BF02760635