Fonctions L des variétés de Deligne-Lusztig et descente de Shintani

François Digne; Jean Michel

Mémoires de la Société Mathématique de France (1985)

  • Volume: 20, page 1-144
  • ISSN: 0249-633X

How to cite

top

Digne, François, and Michel, Jean. "Fonctions $L$ des variétés de Deligne-Lusztig et descente de Shintani." Mémoires de la Société Mathématique de France 20 (1985): 1-144. <http://eudml.org/doc/94859>.

@article{Digne1985,
author = {Digne, François, Michel, Jean},
journal = {Mémoires de la Société Mathématique de France},
keywords = {L-functions; Deligne-Lusztig varieties; reductive group; characters of the Hecke algebra; group of rational points; decomposition of Shintani descents of unipotent characters},
language = {fre},
pages = {1-144},
publisher = {Société mathématique de France},
title = {Fonctions $L$ des variétés de Deligne-Lusztig et descente de Shintani},
url = {http://eudml.org/doc/94859},
volume = {20},
year = {1985},
}

TY - JOUR
AU - Digne, François
AU - Michel, Jean
TI - Fonctions $L$ des variétés de Deligne-Lusztig et descente de Shintani
JO - Mémoires de la Société Mathématique de France
PY - 1985
PB - Société mathématique de France
VL - 20
SP - 1
EP - 144
LA - fre
KW - L-functions; Deligne-Lusztig varieties; reductive group; characters of the Hecke algebra; group of rational points; decomposition of Shintani descents of unipotent characters
UR - http://eudml.org/doc/94859
ER -

References

top
  1. [A] D. ALVISDuality in the Character Ring of Finite Chevalley Groups. Proc. of Symposia in Pure Mathematics, vol.37 pp.353-357. Zbl0452.20005MR82c:20015
  2. [AS1] T. ASAIOn the Zeta Functions of the Varieties X(w) of the Split Classical Groups and the Unitary Groups, Osaka Math. J. 20 (1983) pp.21-32. Zbl0515.20026MR85a:20020
  3. [AS2] T. ASAIUnipotent Class Functions of Split Orthogonal Groups SO+2n over Finite Fields. Communications in Algebra, 12 (1984) pp. 517-615. Zbl0545.20028MR86a:20044
  4. [AS3] T. ASAIThe Unipotent Class Functions on the Symplectic and Odd Orthogonal Groups over Finite Fields. Communications in Algebra, 12 (1984) pp.617-645. Zbl0559.20024MR86a:20045
  5. [AS4] T. ASAIUnipotent Class Functions of Exceptionnal Groups over Finite Fields. Communications in Algebra, 12 (1984) pp.2729-2857. Zbl0547.20037MR86a:20046
  6. [BBK1] N. BOURBAKIGroupes et Algèbres de Lie, Chapitres IV, V, VI (Hermann). Zbl0186.33001
  7. [BBK2] N. BOURBAKIAlgèbre, Chapitre VIII (Hermann). 
  8. [BC] C.T. BENSONC.W. CURTISOn the Degree and Rationality of Certain Characters of Finite Chevalley Groups. Transaction of the American Mathematical Society, 165 (1972) pp.251-273. Zbl0246.20008MR46 #3608
  9. [BT] A. BOREL et J. TITSGroupes Réductifs. Publications Mathématiques de l'IHES n° 27 (1965) pp.55-160. Zbl0145.17402MR34 #7527
  10. [C] C.W. CURTISTruncation and Duality in the Character Ring of a Finite Group of Lie Type. J. of Algebra, 62 (1980) pp.320-332. Zbl0426.20006MR81e:20011
  11. [CH] B. CHANGThe Conjugacy Classes of Chevalley Groups of Type G2. J. of Algebra 9 (1968) pp.190-211. Zbl0285.20043MR37 #2843
  12. [CHR] B. CHANG et R. REEThe Characters of G2(q). Symp. Math. 13, Gruppi Abeliani, Gruppi e loro Rappresent. Convegni 1972 pp.395-413. Zbl0314.20034MR51 #673
  13. [CIK] C.W. CURTIS, N. IWAHORI, R. KILMOYERHecke Algebras and Characters of Parabolic Type of Finite Groups with (B, N) Pairs. Publ. Math. de l'IHES n° 40 pp.81-116. Zbl0254.20004MR50 #494
  14. [CR1] C.W. CURTIS, I. REINERRepresentation Theory of Finite Groups and Associative Algebras (Interscience 1966). Zbl0131.25601
  15. [CR2] C.W. CURTIS, I. REINERMethods of Representation Theory with Applications to Finite Groups and Orders, Volume I (Interscience 1981). Zbl0469.20001
  16. [D] M. DEMAZUREDésingularisation des Variétés de Schubert Généralisées. Annales de l'ENS tome 7 (1974) pp.53-88. Zbl0312.14009MR50 #7174
  17. [DL] P. DELIGNE, G. LUSZTIGRepresentations of Reductive Groups over Finite Fields. Annals of Math. 103 (1976) pp.103-161. Zbl0336.20029MR52 #14076
  18. [DL2] P. DELIGNE, G. LUSZTIGDuality for Representations of a Reductive Group over a Finite Field II. J. of Algebra 81 (1983) pp.540-545. Zbl0535.20020MR85b:20058
  19. [DM1] F. DIGNE et J. MICHELDescente de Shintani des Caractères d'un Groupe de Chevalley Fini. Comptes Rendus de l'Académie des Sciences t.291 (17 novembre 1980) pp.571-574. Zbl0456.20021MR82b:20065
  20. [DM2] F. DIGNE et J. MICHELDescente de Shintani des Caractères de Deligne-Lusztig. Comptes Rendus de l'Académie des Sciences t.291 (15 décembre 1980) pp.651-653. Zbl0456.20020MR82a:20053
  21. [DM3] F. DIGNE et J. MICHELRemarque sur la Dualité de Curtis. J. of Algebra 79 (1982) pp.151-160. Zbl0493.20026MR85c:20036
  22. [DM4] F. DIGNE et J. MICHELThéorie de Deligne-Lusztig et Caractères des Groupes Linéaires et Unitaires. Publications de l'Equipe de la Théorie des Groupes Finis (ERA 944, Université Paris VII et ENSJF) février 1983. A paraître au J. of Algebra. Zbl0622.20034
  23. [DM5] F. DIGNE et J. MICHELNombre de Points Rationnels des Variétés de Deligne-Lusztig et Caractères de l'Algèbre de Hecke. Comptes Rendus de l'Académie des Sciences t.287 (6 novembre 1978) pp.811-814. Zbl0425.20039MR80h:20067
  24. [FR] J.S. FRAMEThe Classes and Representations of the Groups of 27 Lines and 28 Bitangents. Annali di Matematica 32 (1951) pp. 83-169. Zbl0045.00505MR13,817i
  25. [K1] N. KAWANAKAOn the Irreducible Characters of Finite Unitary Groups. J. of Math. Society of Japan 29 (1977) pp. 425-450. Zbl0353.20031MR56 #8678
  26. [K2] N. KAWANAKALifting of Irreducible Characters of Finite Classical Groups I. J. Faculty of Science, Univ. Tokyo 28 (1982) pp. 851-861. Zbl0499.20027MR83g:20047
  27. [K3] N. KAWANAKALifting of Irreducible Characters of Finite Classical Groups II. Journal of the Faculty of Science Univ. of Tokyo 30 (1984) pp. 499-516. Zbl0536.20023MR85f:20037
  28. [L1] G. LUSZTIGRepresentations of Finite Chevalley Groups. CBMS Regional Conference Series in Math. n° 39 AMS, 1978. Zbl0418.20037MR80f:20045
  29. [L2] G. LUSZTIGCoxeter Orbits and Eigenspaces of Frobenius. Inventiones Math. 28 (1976) pp. 101-159. Zbl0366.20031MR56 #12138
  30. [L3] G. LUSZTIGCharacters of Reductive Groups over a Finite Field. Annals of Math. Studies 107 Princeton University Press. Zbl0556.20033MR86j:20038
  31. [L4] G. LUSZTIGOn the Finiteness of the Number of Unipotent Classes. Inventiones Math. 34 (1976) pp.201-213. Zbl0371.20039MR54 #7653
  32. [L5] G. LUSZTIGUnipotent Representations of a Finite Chevalley Group of Type E8. Quarterly Journal of Math. Oxford 30 (1979) pp.315-338. Zbl0418.20038MR80j:20041
  33. [L6] G. LUSZTIGIrreducible Representations of Finite Classical Groups. Inventiones Math. 43 (1977) pp.125-175. Zbl0372.20033MR57 #3228
  34. [L7] G. LUSZTIGUnipotent Characters of the Symplectic and Odd Orthogonal Groups over a Finite Field. Inventiones Math. 64 (1981) pp.263-296. Zbl0477.20023MR83b:20011
  35. [L8] G. LUSZTIGUnipotent Characters of the Even Orthogonal Groups Over a Finite Field. Transactions of the American Math. Society n° 2 pp.733-751. Zbl0491.20034MR83i:20035
  36. [L9] G. LUSZTIGOn the Unipotent Characters of the Exceptionnal Groups Over Finite Fields. Inventiones Math. 60 (1980) pp.173-192. Zbl0443.20036MR82c:20081
  37. [LS] G. LUSZTIG et N. SPALTENSTEINInduced Unipotent Classes. J. of the London Math. Society 19 (1979) pp.41-52. Zbl0407.20035MR82g:20070
  38. [RO] G. C. ROTATheory of Möbius Functions. Z. Wahrscheinlichkeitstheorie 2 (1964) pp.340-368. Zbl0121.02406MR30 #4688
  39. [SB] A. BOREL et al.Seminar on Algebraic Groups and Related Finite Groups. Lecture Notes in Mathematics n° 131 (Springer). Zbl0192.36201
  40. [SGA] SGA 4½ et SGA 5Cohomologie Etale, Lecture Notes in Math. n° 569 ; Cohomologie l-adique et Fonctions L, Lecture Notes in Math. n°589. Zbl0345.00011
  41. [SH] T. SHINTANITwo Remarks on Irreducible Characters of Finite General Linear Groups. J. Math. Society of Japan 28 (1976) pp.396-414. Zbl0323.20041MR54 #2825
  42. [ST] B. SRINIVASANRepresentations of Finite Chevalley Groups. Lecture Notes in Mathematics n° 764 (Springer). Zbl0434.20022MR83a:20054
  43. [ZH] A. ZHELEVINSKIRepresentations of Finite Classical Groups. Lecture Notes in Math. n° 869 (Springer). Zbl0465.20009

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.