Détermination des caractères des groupes finis simples : travaux de Lusztig

Pierre Cartier

Séminaire Bourbaki (1985-1986)

  • Volume: 28, page 137-161
  • ISSN: 0303-1179

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Cartier, Pierre. "Détermination des caractères des groupes finis simples : travaux de Lusztig." Séminaire Bourbaki 28 (1985-1986): 137-161. <http://eudml.org/doc/110058>.

@article{Cartier1985-1986,
author = {Cartier, Pierre},
journal = {Séminaire Bourbaki},
keywords = {irreducible characters; finite groups of Lie type; connected reductive group; Frobenius map; maximal torus; Borel subgroup; Deligne-Lusztig virtual characters; -adic cohomology; semisimple classes; Jordan decomposition; irreducible constituents},
language = {fre},
pages = {137-161},
publisher = {Société Mathématique de France},
title = {Détermination des caractères des groupes finis simples : travaux de Lusztig},
url = {http://eudml.org/doc/110058},
volume = {28},
year = {1985-1986},
}

TY - JOUR
AU - Cartier, Pierre
TI - Détermination des caractères des groupes finis simples : travaux de Lusztig
JO - Séminaire Bourbaki
PY - 1985-1986
PB - Société Mathématique de France
VL - 28
SP - 137
EP - 161
LA - fre
KW - irreducible characters; finite groups of Lie type; connected reductive group; Frobenius map; maximal torus; Borel subgroup; Deligne-Lusztig virtual characters; -adic cohomology; semisimple classes; Jordan decomposition; irreducible constituents
UR - http://eudml.org/doc/110058
ER -

References

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  1. [1] A. Borel (éditeur) - Seminar on algebraic groups and related finite groups, Lect. Notes in Math., 131(1970), Springer, Berlin. Zbl0192.36201MR258838
  2. [2] N. Bourbaki - Groupes et Algèbres de Lie, chap. 4 à 6, Masson, Paris, 1981. Zbl0483.22001MR647314
  3. [3] N. Bourbaki - Groupes et Algèbres de Lie, chap. 7 et 8, Hermann, Paris, 1975. Zbl0483.22001MR453824
  4. [4] R.W. Carter - Simple groups of Lie type, Wiley, New York, 1972. Zbl0723.20006MR407163
  5. [5] R.W. Carter - Finite groups of Lie type : conjugacy classes and complex characters, Wiley-Interscienoe, New York, 1985. Zbl0567.20023MR794307
  6. [6] D. Gorenstein - Finite simple groups, an introduction to their classification, Plenum Press, New York, 1982. Zbl0483.20008MR698782
  7. [7] R. Steinberg - Lectures on Chevalley groups, Yale University, 1967. MR466335
  8. [8] J.-L. Brylinski - (Co)-homologie d'intersection et faisceaux pervers, exposé n° 585, Astérisque92-93(1982). Zbl0574.14017MR689529
  9. [9] J.-P. Serre - Représentations linéaires des groupes finis "algébriques" [d'après Deligne - Lusztig], exposé n° 487, Lect. Notes in Math., 567(1977), Springer. Zbl0367.20045MR435240
  10. [10] T.A. Springer - Caractères de groupes de Chevalley finis, exposé n° 429, Lect. Notes in Math., 383(1974), Springer. Zbl0296.20019MR463276
  11. [11] T.A. Springer - Quelques applications de la cohomologie d'intersection, exposé n° 589, Astérisque105-106(1983). Zbl0526.22014
  12. [12] G. Lusztig - The discrete series of GLn over a finite field, Annals of Mathematics Studies, 81(1974), Princeton University Press. Zbl0293.20038MR382419
  13. [13] G. Lusztig - On the Green polynomials of classical groups, Proc. London Math. Soc., 33(1976), p. 443-475. Zbl0371.20037MR424959
  14. [ 14] G. Lusztig - Coxeter orbits and eigenspaces of Frobenius, Invent. Math., 38 (1976/77), p. 101-159. Zbl0366.20031MR453885
  15. [15] G. Lusztig - Representations of finite Chevalley groups, CBMS Regional Conference Series in Mathematics (A.M.S.), 39(1977). Zbl0418.20037MR518617
  16. [16] G. Lusztig - On the finiteness of the number of unipotent classes, Invent. Math., 34(1976), p. 201-213. Zbl0371.20039MR419635
  17. [17] G. Lusztig - Characters of reductive groups over a finite field, Annals of Math. Studies, 107(1984), Princeton University Press. Zbl0556.20033MR742472
  18. [18] G. Lusztig - Intersection cohomology complexes on a reductive group, Invent. Math., 75(1984), p. 205-272. Zbl0547.20032MR732546
  19. [19] G. Lusztig - Left cells in Weyl groups, Lect. Notes in Math., 1024(1983), Springer. Zbl0537.20019MR727851
  20. [20] G. Lusztig - Characters of reductive groups over finite fields, Proceedings of the Int. Congress of Math., Warszawa, 1983, p. 877-880. Zbl0572.20026MR804741
  21. [21] G. Lusztig et D. Vogan - Singularities of closures of K-orbits on a flag manifold, Invent. Math., 71 (1983) , p. 365-379. Zbl0544.14035MR689649
  22. [22] P. Deligne et G. Lusztig - Representations of reductive groups over finite fields, Ann. of Math., 103(1976)., p. 103-161. Zbl0336.20029MR393266
  23. [23] J.A. Green - The characters of the finite linear groups, Trans. Amer. Math. Soc., 80(1955), p. 402-447. Zbl0068.25605MR72878
  24. [24] T. Shoji - On the Springer representations of the Weyl groups of classical algebraic groups, Comm. Algebra, 7(1979), p. 1713-1745 (et corrections p. 2027-2033). Zbl0426.20028MR546195
  25. [25] T.A. Springer - Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. Math., 36(1976), p. 173-207. Zbl0374.20054MR442103
  26. [26] T.A. Springer - A construction of representations of Weyl groups, Invent. Math., 44(1978), p. 279-293. Zbl0376.17002MR491988
  27. [27] T. Asai - On the zeta functions of the varieties X(w) of the split classical groups and the unitary groups, Osaka J. Math., 20(1983), p. 21-32. Zbl0515.20026MR695614
  28. [28] C.T. Benson et C.W. Curtis - On the degrees and rationality of certain characters of finite Chevalley groups, Trans. Amer. Math. Soc., 165 (1972) , p. 251-273 et 202(1975), p. 405-406. Zbl0246.20008MR304473
  29. [29] C.W. Curtis, N. Iwahori, R. Kilmoyer - Hecke algebras and characters of parabolic type of finite groups with (BN) pairs, Publ. Math. IHES, 40(1972), p. 81-116. Zbl0254.20004MR347996
  30. [30] F. Digne et J. Michel - Descente de Shintani des caractères d' un groupe de Chevalley fini, C.R. Acad. Sci. Paris, t. 287 (1978), Série A, p. 811-814. Zbl0425.20039
  31. [31] P.N. Hoefsmit - Representations of Hecke algebras of finite groups with BN-pairs of classical type, Ph.D. thesis, Univ. of British Columbia, Vancouver, 1974. 
  32. [32] R.B. Howlett et G.I. Lehrer - Induced cuspidal representations and generalized Hecke rings, Invent. Math., 58(1980), p. 37-64. Zbl0435.20023MR570873
  33. [33] N. Iwahori - On the structure of a Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo, 10(1964), p. 215-236. Zbl0135.07101MR165016
  34. [34] A.A. Beilinson, J. Bernstein et P. Deligne - Faisceaux pervers, Astérisque100(1982). Zbl0536.14011MR751966
  35. [35] A. Borel et al. - Intersection cohomology, Progress in Math., vol. 50(1984), Birkhaüser, Boston. Zbl0553.14002MR788171
  36. [36] P. Deligne - SGA 41/2, Cohomologie étale, Lecture Notes in Math., 569 (1977) , Springer. Zbl0349.14008MR463174
  37. [37] P. Deligne - La conjecture de Weil, I et II, Publ. Math. IHES, 43(1974), p. 273-307 et 52(1980), p. 137-252. Zbl0456.14014MR340258
  38. [38] J.S. Milne - Etale cohomology, Princeton University Press, 1980. Zbl0433.14012MR559531

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