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Coxeter orbits and eigenspaces of Frobenius. (English) Zbl 0366.20031


MSC:

20G40 Linear algebraic groups over finite fields
14F30 \(p\)-adic cohomology, crystalline cohomology
14L99 Algebraic groups
16Gxx Representation theory of associative rings and algebras
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References:

[1] Borel, A., Tits, J.: Groupes réductifs. Publ. Math. I.H.E.S.27, 55-151 (1965) · Zbl 0145.17402
[2] Bourbaki, N.: Groupes et algèbres de Lie. Chap. 4. 5 et 6. Paris: Hermann 1968 · Zbl 0186.33001
[3] Carter, R. W.: Conjugacy classes in the Weyl group. Comp. Math.25, 1, 1-59 (1972) · Zbl 0254.17005
[4] Coxeter, H.S.M.: Discrete groups generated by reflections. Ann. of Math.35, 588-621 (1934) · Zbl 0010.01101 · doi:10.2307/1968753
[5] Curtis, C. W., Iwahori, N., Kilmoyer, R.: Hecke algebras and characters of parabolic type ... Publ. Math. I.H.E.S.40, 81-116 (1972) · Zbl 0254.20004
[6] Deligne, P.: La conjecture de Weil. I. Publ. Math. I.H.E.S.43, 273-307 (1974) · Zbl 0287.14001
[7] 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
[8] Grothendieck, A.: Formule de Lefschetz et rationalité des fonctionsL Séminaire Bourbaki, 279
[9] Harish Chandra: Eisenstein series over finite fields. Funct. Analysis and Related Fields. ed. F.E. Browder. Berlin-Göttingen-Heidelberg: Springer 1970 · Zbl 0226.20049
[10] Katz, N., Messing, W.: Some consequences of the Riemann Hypothesis for varieties over finite fields. Inv. Math.23, 73-77 (1974) · Zbl 0275.14011 · doi:10.1007/BF01405203
[11] Lusztig, G.: On the Green polynomials of classical groups. To appear in the Proc. of L.M.S. · Zbl 0371.20037
[12] Lusztig, G.: Sur la conjecture de Macdonald, C.R. Acad. Sci. Paris, t.280 (10Fév. 1975). 317-320
[13] Solomen, L.: A decomposition of the group algebra of a finite Coxeter group. J. Algebra9, 220-239 (1968) · Zbl 0186.04503 · doi:10.1016/0021-8693(68)90022-7
[14] Springer, T.A.: On the characters of certain finite groups. Proc. Summer School. Budapest 1971 · Zbl 0224.05002
[15] Springer, T.A.: Regular elements in reflection groups. Inv. Math.25, 159-198 (1974) · Zbl 0287.20043 · doi:10.1007/BF01390173
[16] Springer, T.A.: Some arithmetical results on semisimple Lie algebras. Publ. Math. I.H.E.S.30, 115-141 (1966) · Zbl 0156.27002
[17] Steinberg, R.: Endomorphisms of linear algebraic groups. Memoirs of A.M.S.80, 1968 · Zbl 0164.02902
[18] Steinberg, R.: Finite reflection groups. Trans. A.M.S.91, 493-504 (1959) · Zbl 0092.13904 · doi:10.1090/S0002-9947-1959-0106428-2
[19] Steinberg, R.: Lectures on Chevalley groups. Yale University, 1967 · Zbl 0164.34302
[20] Steinberg, R.: Regular elements in semisimple algebraic groups. Publ. Math. I.H.E.S.25, 49-80 (1965) · Zbl 0136.30002
[21] Tits, J.: Classification of algebraic semisimple groups. Proc. Symp Pure Math., vol. 9 A.M.S., 1966 · Zbl 0238.20052
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