Towards the Kazhdan-Lusztig conjecture

O. Gabber; A. Joseph

Annales scientifiques de l'École Normale Supérieure (1981)

  • Volume: 14, Issue: 3, page 261-302
  • ISSN: 0012-9593

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Gabber, O., and Joseph, A.. "Towards the Kazhdan-Lusztig conjecture." Annales scientifiques de l'École Normale Supérieure 14.3 (1981): 261-302. <http://eudml.org/doc/82075>.

@article{Gabber1981,
author = {Gabber, O., Joseph, A.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Kazhdan-Lusztig conjecture; enveloping algebra; complex semisimple Lie algebra; multiplicities; composition series of Verma modules; Bernstein- Gelfand-Gelfand category; extension groups; Jantzen filtration; Kazhdan- Lusztig polynomial},
language = {eng},
number = {3},
pages = {261-302},
publisher = {Elsevier},
title = {Towards the Kazhdan-Lusztig conjecture},
url = {http://eudml.org/doc/82075},
volume = {14},
year = {1981},
}

TY - JOUR
AU - Gabber, O.
AU - Joseph, A.
TI - Towards the Kazhdan-Lusztig conjecture
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1981
PB - Elsevier
VL - 14
IS - 3
SP - 261
EP - 302
LA - eng
KW - Kazhdan-Lusztig conjecture; enveloping algebra; complex semisimple Lie algebra; multiplicities; composition series of Verma modules; Bernstein- Gelfand-Gelfand category; extension groups; Jantzen filtration; Kazhdan- Lusztig polynomial
UR - http://eudml.org/doc/82075
ER -

References

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  1. [1] I. N. BERNSTEIN, I. M. GELFAND and S. I. GELFAND, Category of ɡ Modules (Funct. Anal. Priloz., Vol. 10, 1976, pp. 1-8). Zbl0353.18013MR53 #10880
  2. [2] I. N. BERNSTEIN and S. I. Gelfand, Tensor Products of Finite and Infinite Dimensional Representations of Semisimple Lie Algebras (Compos. Math., Vol. 41, 1980, pp. 245-285). Zbl0445.17006MR82c:17003
  3. [3] N. BOURBAKI, Groupes et algèbres de Lie, Chap. 4-6, Éléments de mathématiques, XXXIV, Hermann, Paris, 1968. 
  4. [4] H. CARTAN and S. EILENBERG, Homological Algebra, Princeton, New Jersey, 1976. 
  5. [5] P. DELORME, Extensions dans la catégorie ϑ de Bernstein-Gelfand-Gelfand. Applications, preprint, Paris, 1978. 
  6. [6] J. DIXMIER, Algèbres enveloppantes, cahiers scientifiques, XXXVII, Gauthier-Villars, Paris, 1974. Zbl0308.17007MR58 #16803a
  7. [7] O. GABBER and A. JOSEPH, The Bernstein-Gelfand-Gelfand Resolution and the Duflo Sum Formula (Compos. Math., Vol. 43, 1981, pp. 107-131). Zbl0461.17004MR82k:17009
  8. [8] J.-C. JANTZEN, Zur Charackterformel gewisser Darstellungen halbeinfacher Gruppen und Lie-Algebren (Math. Z., Vol. 140, 1974, pp. 127-149). Zbl0279.20036MR55 #5756
  9. [9] J.-C. JANTZEN, Moduln mit einem höchsten Gewicht, LN 750, Springer-Verlag, Berlin-Heidelberg-New York, 1980. Zbl0426.17001
  10. [10] D. A. KAZHDAN and G. LUSZTIG, Representations of Coxeter Groups and Hecke Algebras (Invent. Math., Vol. 53, 1979, pp. 165-184). Zbl0499.20035MR81j:20066
  11. [11] D. A. KAZHDAN and G. LUSZTIG, Schubert Varieties and Poincaré Duality, preprint, Harvard, 1979. 
  12. [12] D. VOGAN, Irreducible Characters of Semisimple Lie Groups I (Duke Math. J., Vol. 46, 1979, pp. 61-108). Zbl0398.22021MR80g:22016
  13. [13] D. VOGAN, Irreducible Characters of Semisimple Lie Groups II. The Kazhdan-Lusztig conjectures (Duke Math. J., Vol. 46, 1979, pp. 805-859). Zbl0421.22008MR81f:22024
  14. [14] D. VOGAN, Ordering in the Primitive Spectrum of a Semisimple Lie Algebra (Math. Ann., Vol. 248, 1980, pp. 195-203). Zbl0414.17006MR81k:17006
  15. [15] A. A. BEILINSON and I. N. BERNSTEIN, C. R. Acad. Sc. (to appear). 
  16. [16] J.-L. BRYLINSKI and M. KASHIWARA, Démonstration de la conjecture de Kazhdan-Lusztig sur les modules de Verma [C. R. Acad. Sc. (to appear)]. Zbl0457.22012
  17. [17] J.-L. BRYLINSKI and M. KASHIWARA, Kazhdan-Lusztig Conjecture and Holonomic Systems [Invent. Math. (to appear)]. Zbl0473.22009
  18. [18] S. GELFAND and R. MACPHERSON, Verma Modules and Schubert cells, Preprint, I.H.E.S., November 1980. 
  19. [19] A. JOSEPH. Goldie Rank in the Enveloping Algebra of a Semisimple Lie Algebra, III [J. Alg. (in the press)]. Zbl0482.17002

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