La théorie des blocs et les groupes génériques

Pierre Cartier

Séminaire Bourbaki (1993-1994)

  • Volume: 36, page 171-208
  • ISSN: 0303-1179

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Cartier, Pierre. "La théorie des blocs et les groupes génériques." Séminaire Bourbaki 36 (1993-1994): 171-208. <http://eudml.org/doc/110183>.

@article{Cartier1993-1994,
author = {Cartier, Pierre},
journal = {Séminaire Bourbaki},
keywords = {blocks; defect groups; perfect isometries; isotypies; root data; automorphism groups; Weyl groups; generic groups; connected reductive algebraic groups; finite reductive groups; order polynomials; cyclotomic polynomials; generic subgroups; Levi subgroups; unipotent characters; Deligne-Lusztig virtual characters},
language = {fre},
pages = {171-208},
publisher = {Société Mathématique de France},
title = {La théorie des blocs et les groupes génériques},
url = {http://eudml.org/doc/110183},
volume = {36},
year = {1993-1994},
}

TY - JOUR
AU - Cartier, Pierre
TI - La théorie des blocs et les groupes génériques
JO - Séminaire Bourbaki
PY - 1993-1994
PB - Société Mathématique de France
VL - 36
SP - 171
EP - 208
LA - fre
KW - blocks; defect groups; perfect isometries; isotypies; root data; automorphism groups; Weyl groups; generic groups; connected reductive algebraic groups; finite reductive groups; order polynomials; cyclotomic polynomials; generic subgroups; Levi subgroups; unipotent characters; Deligne-Lusztig virtual characters
UR - http://eudml.org/doc/110183
ER -

References

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  1. [A1] A. Borel - Linear algebraic groups, Grad. Texts Math.126, Springer, 1991. Zbl0726.20030MR1102012
  2. [A2] A. Borel et J. Tits - Groupes réductifs, Publ. Math. I.H.E.S.27 (1965), 55-151. Zbl0145.17402MR207712
  3. [A3] N. Bourbaki - Groupes et algèbres de Lie, Chap. 4, 5 et 6, réimpression, Masson, 1981. Zbl0483.22001MR647314
  4. [A4] N. Bourbaki - Groupes et algèbres de Lie, Chap. 7 et 8, réimpression, Masson, 1990. 
  5. [A5] R.W. Carter - Simple Groups of Lie Type, Wiley, 1972. Zbl0723.20006MR407163
  6. [A6] R.W. Carter - Finite Groups of Lie Type : Conjugacy Classes and Complex Characters, Wiley, 1985. Zbl0567.20023MR794307
  7. [A7] M. Demazure - Données radicielles, Exposé XXI, Schémas en groupes III, un séminaire dirigé par M. Demazure et A. Grothendieck, Lect. Notes in Math.153 (1970), Springer. MR274458
  8. [A8] F. Digne et J. Michel - Representations of finite groups of Lie type, Cambridge Univ. Press, 1991. Zbl0815.20014MR1118841
  9. [A9] J. Humphreys - Linear algebraic groups, Grad. Texts Math.21, Springer, 1975. Zbl0325.20039MR396773
  10. [A10] G. Lusztig - Characters of reductive groups over a finite field, Ann. Math. Studies107, Princeton Univ. Press, 1984. Zbl0556.20033MR742472
  11. [A11] T.A. Springer - Linear algebraic groups, Prog. Math.9, Birkhaüser, 1981. Zbl0453.14022MR632835
  12. [A12] T.A. Springer et R. Steinberg - Conjugacy classes, in Borel et al., Seminar on algebraic groups and related finite groups, Lect. Notes in Math.131 (1970), Springer. Zbl0249.20024MR268192
  13. [A13] R. Steinberg - Endomorphisms of linear algebraic groups, A.M.S. Memoirs80 (1968). Zbl0164.02902MR230728
  14. [A14] R. Steinberg - Lectures on Chevalley groups, Yale University, 1967. MR466335
  15. [A15] C. Chevalley - Théorie des blocs, Sém. Bourbaki, exp. n° 419, Lect. Notes in Math.383 (1974), Springer. Zbl0302.20016MR422397
  16. [A16] C.W. Curtis et I. Reiner - Methods in representation theory, I, II, Wiley, 1981/1987. Zbl0616.20001
  17. [A17] W. Feit - The representation theory of finite groups, North-Holland Publ., 1982. Zbl0493.20007MR661045
  18. [A18] J.-P. Serre - Représentations linéaires des groupes finis, Hermann, 1978. Zbl0407.20003MR543841
  19. [B1] T.A. Springer - Caractères de groupes de Chevalley finis, exp. n° 429, Lect. Notes in Math.383 (1974), Springer. Zbl0296.20019MR463276
  20. [B2] J.-P. Serre - Représentations linéaires des groupes finis "algébriques" [d'après Deligne-Lusztig], exp. n° 487, Lect. Notes in Math. 567 (1977), Springer. Zbl0367.20045MR435240
  21. [B3] P. Cartier - Détermination des caractères des groupes finis simples : travaux de Lusztig, exp. n° 658, Astérisque145-146 (1987), 137-161. Zbl0618.20034MR880030
  22. [B4] P. Deligne et G. Lusztig - Representations of reductive groups over finite fields, Annals of Math.103 (1976), 103-161. Zbl0336.20029MR393266
  23. [B5] F. Digne et J. Michel - Théorie de Deligne-Lusztig et caractères des groupes linéaires et unitaires, J. of Algebra107 (1987), 217-255. Zbl0622.20034MR883883
  24. [B6] Harish- Chandra - Eisenstein series over finite fields, in "Functional analysis and related fields" (F.E. Browder, édit.), pages 76 à 88, Springer, 1970. Zbl0226.20049MR457579
  25. [B7] P.N. Hoefsmit - Representations of Hecke algebras of finite groups with BN-pairs of classical type, Ph.D. Thesis, Univ. of British Columbia (1974). 
  26. [B8] R.B. Howlett et G.I. Lehrer - Induced cuspidal representations and generalized Hecke rings, Invent. Math.58 (1980), 37-64. Zbl0435.20023MR570873
  27. [B9] R.B. Howlett et G.I. Lehrer - Representations of generic algebras and finite groups of Lie type, Trans. Amer. Math. Soc.280 (1983), 753-779. Zbl0537.20018MR716849
  28. [B10] G. Lusztig - Irreducible representations of finite classical groups, Invent. Math.43 (1977), 125-175. Zbl0372.20033MR463275
  29. [C1] C. Chevalley - Invariants of finite groups generated by reflections, Amer. J. Math.77 (1955), 778-782. Zbl0065.26103MR72877
  30. [C2] A.M. Cohen - Finite complex refiection groups, Ann. Sci. E.N.S.9 (1976), 379-436. Zbl0359.20029MR422448
  31. [C3] H.S.M. Coxeter - Finite groups generated by unitary reflections, Abh. math. Sem. Univ. Hamburg31 (1967), 125-135. Zbl0189.32302MR230800
  32. [C4] L.L. Grove et C.T. Benson - Finite reflection groups, Grad. Texts Math.99, Springer, 1985. Zbl0579.20045MR777684
  33. [C5] G.C. Shephard et J.A. Todd - Finite unitary reflection groups, Canad. J. Math.6 (1954), 274-304. Zbl0055.14305MR59914
  34. [C6] T.A. Springer - Regular elements of finite reflection groups, Invent. Math.25 (1974), 159-198. Zbl0287.20043MR354894
  35. [D1] R. Boyce - Cyclotomic polynomials and irreducible representations of finite groups of Lie type, manuscrit non publié. 
  36. [D2] M. Broué - Les l-blocs des groupes GL(n, q) et U(n, q2) et leurs structures locales, Sém. Bourbaki, exp. n° 640, Astérisque133-134 (1986), 159-188. Zbl0653.20041MR837219
  37. [D3] M. Broué et J. Michel - Blocs et séries de Lusztig dans un groupe réductif fini, J. reine angew. Math.395 (1989), 56-67. Zbl0654.20048MR983059
  38. [D4] M. Broué et G. Malle - Théorèmes de Sylow génériques pour les groupes réductifs sur les corps finis, Math. Ann.292 (1992), 241-262. Zbl0820.20057MR1149033
  39. [D5] M. Broué et G. Malle - Zyklotomische Hecke Algebren, Astérisque212 (1993), 119-189. Zbl0835.20064MR1235834
  40. [D6] M. Broué et J. Michel - Blocs à groupes de défaut abéliens des groupes réductifs finis, Astérisque212 (1993), 93-117. Zbl0832.20024MR1235833
  41. [D7] M. Broué, G. Malle et J. Michel - Generic blocks of finite reductive groups, Astérisque212 (1993), 7-92. Zbl0843.20012MR1235832
  42. [D8] M. Cabanes et M. Enguehard - On unipotent blocks of finite reductive groups of a given type, Math. Z.213 (1993), 479-490. Zbl0795.20021MR1227495
  43. [D9] M. Cabanes et M. Enguehard - On unipotent blocks and their ordinary characters, Invent. Math.117 (1994), 149-164. Zbl0817.20046MR1269428
  44. [D10] M. Cabanes et M. Enguehard - On general blocks of finite reductive groups : ordinary characters and defect groups, Publications du LMENS, 93- 13 (1993). 
  45. [D11] P. Fong et B. Srinivasan - The blocks of finite general and unitary groups, Invent. Math.69 (1982), 109-153. Zbl0507.20007MR671655
  46. [D12] P. Fong et B. Srinivasan - The blocks of finite classical groups, J. reine angew. Math.396 (1989), 122-191. Zbl0656.20039MR988550
  47. [D13] P. Fong et B. Srinivasan - Generalized Harish-Chandra theory for unipotent characters of finite classical groups, J. of Algebra104 (1986), 301-309. Zbl0606.20035MR866777
  48. [D14] M. Geck - A classification of l-blocks of finite groups of Lie type, J. of Algebra151 (1992), 180-191. Zbl0771.20007MR1182021
  49. [D15] G. Hiss - Zerlegungszahlen endlicher Gruppen vom Lie-Typ in nicht-definierender Charakteristik, thèse, 1990. Zbl0832.20021
  50. [D16] G. Lusztig - Coxeter groups and unipotent representations, Astérisque212 (1993), 191-203. Zbl0853.20030MR1235835
  51. [D17] G. Lusztig - Exotic Fourier transform (with an Appendix by G. Malle), Duke Math. Journ.73 (1994), 227-248. Zbl0815.20031MR1257284
  52. [D18] Ll. Puig - Algèbres de sources de certains blocs des groupes de Chevalley, Astérisque181-182 (1990), 221-236. Zbl0773.20002MR1051252
  53. [D19] K. Schewe - Blöcke exzeptionneller Chevalley-Gruppen, Bonner Math. Schriften165, Bonn, 1985. Zbl0644.20027MR825237
  54. [E1] J.L. Alperin et M. Broué - Local Methods in Block Theory, Annals of Math.110 (1979), 143-157. Zbl0416.20006MR541333
  55. [E2] M. Broué - Théorie locale des blocs, Proceedings of the International Congress of Mathematicians, Berkeley (1986), vol. 1, 360-368. Zbl0663.20007MR934235
  56. [E3] M. Broué - Isométries parfaites, types de blocs, catégories dérivées, Astérisque181-182 (1990), 61-92. Zbl0704.20010MR1051243
  57. [E4] M. Broué - Isométries de caractères et équivalences de Morita ou dérivées, Publ. Math. I.H.E.S.71 (1990), 45-63. Zbl0727.20005MR1079643
  58. [E5] M. Broué - Equivalence of blocks of group algebras, dans "Finite dimensional algebras and related topics", (V. Dlab et L. Scott édit.), Kluwer Acad. Publ., 1994. Zbl0827.20007MR1308977
  59. [E6] M. Broué - Rickard equivalence and block theory, Publications du LMENS, 94-1 (1994). Zbl0847.20003MR1342782
  60. [E7] M. Broué et Ll. Puig - A Frobenius theorem for blocks, Invent. Math.56 (1980), 117-128. Zbl0425.20008MR558864
  61. [E8] D. Happel - Triangulated Categories in the Representation Theory of Finite Dimensional Algebras, Cambridge Univ. Press, 1988. Zbl0635.16017MR935124
  62. [E9] M. Linckelmann - Derived equivalence for cyclic blocks over a p-adic ring, Math. Z.207 (1991), 293-304. Zbl0714.20006MR1109667
  63. [E10] Ll. Puig - Local block theory in p-solvable groups, B. Cooperstein and G. Mason éd., "The Santa Cruz Conference on Finite Groups", Proc. Symp. Pure Math., vol. XXXVII, Amer. Math. Soc., 1980. Zbl0449.20020MR604608
  64. [E11] Ll. Puig - Nilpotent blocks and their source algebras, Invent. Math.93 (1988), 77-116. Zbl0646.20010MR943924
  65. [E12] Ll. Puig - Local fusion in block source algebras, J. of Algebra104 (1986), 358-369. Zbl0606.20016MR866781
  66. [E13] J. Rickard - Morita Theory for Derived Categories, J. London Math. Soc.39 (1989), 436-456. Zbl0642.16034MR1002456
  67. [E14] J. Rickard - Derived categories and stable equivalences, J. Pure and Appl. Alg.61 (1989), 307-317. Zbl0685.16016MR1027750
  68. [E15] J. Rickard - Derived equivalences as derived functors, J. London Math. Soc.43 (1991), 37-48. Zbl0683.16030MR1099084
  69. [E16] J. Rickard - Finite group actions and etale cohomology, prépublication (1992). 
  70. [E17] R. Rouquier - Isométries parfaites dans les blocs à défaut abélien des groupes symétriques et sporadiques, J. of Algebra168 (1994), 648-694. Zbl0854.20016MR1292784

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