Trigonometric sums, Green functions of finite groups and representations of Weyl groups. (English) Zbl 0374.20054


20G05 Representation theory for linear algebraic groups
20G10 Cohomology theory for linear algebraic groups
Full Text: DOI EuDML


[1] Bala, P., Carter, R. W.: Classes of unipotent elements in simple algebraic groups. To appear · Zbl 0364.22006
[2] Birkes, D.: Orbits of linear algebraic groups. Ann. of Math.93, 459-475 (1971) · Zbl 0212.36402 · doi:10.2307/1970884
[3] Borel, A.: Linear algebraic groups. New York W. A. Benjamin 1969 · Zbl 0206.49801
[4] Borel, A., et al.: Seminar in algebraic groups and related finite groups. Lecture Notes in Math.131. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0192.36201
[5] Bourbaki, N.: Groupes et algebres de Lie, Chap. IV, V, VI, Paris: Hermann 1968 · Zbl 0186.33001
[6] Carter, R. W.: Weyl groups and finite Chevalley groups. Proc. Cambridge Philos. Soc.67, 269-276 (1970) · Zbl 0198.04501 · doi:10.1017/S0305004100045540
[7] Chang, B.: The conjugate classes of Chevalley groups of type (G 2). J. of Algebra9, 190-211 (1968) · Zbl 0285.20043 · doi:10.1016/0021-8693(68)90020-3
[8] Chang, B., Ree, R.: The characters ofG 2(q). In: Symposia Mathematica, vol. XIII, London and New York: Academic Press 1974 · Zbl 0314.20034
[9] Deligne, P.: La conjecture de Weil I. Publ. Math. I.H.E.S.43, 273-307 (1974) · Zbl 0287.14001
[10] Deligne, P., Lusztig, G.: Representations of reductive groups over finite fields. Ann. of Math.103, 103-161 (1976) · Zbl 0336.20029 · doi:10.2307/1971021
[11] Grothendieck, A.: Formule de Lefschetz et rationalité des fonctionsL, Sém. Bourbaki no. 279, 15 p. New York: W. A. Benjamin 1966
[12] Grothendieck, A.: Eléments de géometrie algébrique, Ch. IV (3me partie). Publ. Math. I.H.E.S.28, 1966
[13] Harish-Chandra: Differential operators on a semisimple Lie algebra. Am. J. of Math.79, 87-120 (1957) · Zbl 0072.01901 · doi:10.2307/2372387
[14] Kac, V., Weisfeiler, B.: Coadjoint action of a semisimple algebraic group and the center of the enveloping algebra in characteristicp. To appear in Proc. Kon. Ak. v. Wet. (Amsterdam) · Zbl 0324.17001
[15] Kazhdan, D.A.: Proof of Springer’s hypothesis. To appear · Zbl 0391.22006
[16] Raynaud, M.: Passage au quotient par une relation d’équivalence plate. In: Proceedings of a conference on Local Fields (Driebergen 1968). pp. 78-85, Berlin-Heidelberg-New York: Springer 1967 · Zbl 0165.24003
[17] SGA1: Revêtements étales et groupe fondamental (séminaire dirigé par A. Grothendieck). Lecture Notes in Math. 224. Berlin-Heidelberg-New York: Springer 1971
[18] SGA3: Schémas en Groupes (séminaire dirigé par A. Grothendieck), Lecture Notes in Math. 151, 152, 153. Berlin-Heidelberg-New York: Springer 1970
[19] SGA4: Théorie des topos et cohomologie étale des schémas (seminaire dirigé par M. Artin, A. Grothendieck et J.L. Verdier), Lecture Notes in Math. 269, 270, 305. Berlin-Heidelberg-New York: Springer 1972/73
[20] Serre, J.-P.: Valeurs propres des endomorphismes de Frobenius (d’après P. Deligne), Sém. Bourbaki, vol. 1973/74, exp. 446. Lecture Notes in Math. 431. Berlin-Heidelberg-New York: Springer 1975
[21] Spaltenstein, N.: The fixed print set of a unipotent transformation on the flag manifold. To appear in Proc. Kon. Ak. v. Wet. (Amsterdam) · Zbl 0343.20029
[22] Speiser, A.: Die Theorie der Gruppen von endlicher Ordnung. 3. Aufl., Grundl. d Math. Wiss., Bd. V. Berlin: Springer 1937 · JFM 63.0059.01
[23] Springer, T. A.: Some arithmetical results on semi-simple Lie algebras. Publ. Math. I.H.E.S.30, 115-141 (1966) · Zbl 0156.27002
[24] Springer, T. A.: The unipotent variety of a semisimple group. In: Algebraic geometry (Papers presented at the Bombay Colloquium) pp. 373-391. Oxford: Oxford University Press 1969
[25] Springer, T. A.: Generalization of Green’s polynomials. In: Representation theory of finite groups and related topics (Proc. Symp. Pure Math. Vol. XXI) pp. 149-153, Amer. Math. Soc. 1971
[26] Springer, T. A.: Regular elements of finite reflection groups. Inventiones math.25, 159-198 (1974) · Zbl 0287.20043 · doi:10.1007/BF01390173
[27] Srinivasan, B.: The characters of the finite symplectic groupSp(4,q). Trans. Amer. Math. Soc.131, 488-525 (1968) · Zbl 0213.30401
[28] Steinberg, R.: Regular elements of semi-simple algebraic groups. Publ. Math. I.H.E.S.25, 49-80 (1965)
[29] Steinberg, R.: Endomorphism of linear algebraic groups, Mem. Am. Math. Soc. no 80, 1968 · Zbl 0164.02902
[30] Steinberg, R.: Conjugacy classes in algebraic groups. Lecture Notes in Math.366, Berlin-Heidelberg-New York: Springer 1974 · Zbl 0281.20037
[31] Steinberg, R.: On the desingularization of the unipotent variety. To appear · Zbl 0352.20035
[32] Stuhler, U.: Unipotente und nilpotente Klassen in einfachen Gruppen und Lie-Algebren vom TypG 2 Proc. Kon. Ak. v. Wet. (Amsterdam)74, 365-378 (1971) · Zbl 0232.20085
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