On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula

O. Gabber; A. Joseph

Compositio Mathematica (1981)

  • Volume: 43, Issue: 1, page 107-131
  • ISSN: 0010-437X

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Gabber, O., and Joseph, A.. "On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula." Compositio Mathematica 43.1 (1981): 107-131. <http://eudml.org/doc/89490>.

@article{Gabber1981,
author = {Gabber, O., Joseph, A.},
journal = {Compositio Mathematica},
keywords = {Bernstein-Gelfand-Gelfand resolution; Duflo sum formula; complex semisimple Lie algebra},
language = {eng},
number = {1},
pages = {107-131},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula},
url = {http://eudml.org/doc/89490},
volume = {43},
year = {1981},
}

TY - JOUR
AU - Gabber, O.
AU - Joseph, A.
TI - On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula
JO - Compositio Mathematica
PY - 1981
PB - Sijthoff et Noordhoff International Publishers
VL - 43
IS - 1
SP - 107
EP - 131
LA - eng
KW - Bernstein-Gelfand-Gelfand resolution; Duflo sum formula; complex semisimple Lie algebra
UR - http://eudml.org/doc/89490
ER -

References

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  1. [1] I.N. Bernstein, I.M. Gelfand and S.I. Gelfand: Category of g modules, Funct. Anal. Priloz., 10 (1976) 1-18. Zbl0353.18013
  2. [2] I.N. Bernstein, I.M. Gelfand and S.I. Gelfand: Differential operators on the base affine space and a study of g modules, In Lie groups and their representations; proceedings, Bolyai János Math. Soc., Budapest, 1971. Ed. I.M. Gelfand, London, Hilger, 1975.]. Zbl0338.58019
  3. [3] I.N. Bernstein and S.I. Gelfand: Tensor products of finite and infinite dimensional representations of semisimple Lie algebras. Compos. Math., 41 (1980) 245-285. Zbl0445.17006MR581584
  4. [4] W. Borho and J.C. Jantzen: Über primitive Ideale in der Einhüllenden einer halbeinfacher Lie-Algebra. Invent. Math., 39 (1977) 1-53. Zbl0327.17002MR453826
  5. [5] N. Conze-Berline and M. Duflo: Sur les représentations induites des groupes semi-simples complexes. Compos. Math., 34 (1977) 307-336. Zbl0389.22016MR439991
  6. [6] P. Delorme: Extensions dans la cátegorie O de Bernstein-Gelfand-Gelfand. Applications, preprint, Paris, 1977. 
  7. [7] J. Dixmier: Algèbres enveloppantes. Cahiers scientifiques, XXXVII, Gauthier-Villars, Paris, 1974. Zbl0308.17007MR498737
  8. [8] M. Duflo: Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple. Ann. Math., 105 (1977) 107-120. Zbl0346.17011MR430005
  9. [9] M. Duflo: Representations irréductibles des groupes semi-simples complexes, in LN 497, Springer-Verlag, Berlin/ Heidelberg/New York, 1975, pp. 26-88. Zbl0315.22008MR399353
  10. [10] O. Gabber and A. Joseph: Towards the Kazhdan-Lusztig conjecture. Ann. Ec. Norm. Sup. (in the press). Zbl0476.17005
  11. [11] J.C. Jantzen: Moduln mit einem höchten Gewicht, LN 750, Springer-Verlag, Berlin/Heidelberg /New York, 1979. Zbl0426.17001MR552943
  12. [12] A. Joseph: On the annihilators of the simple subquotients of the principal series. Ann. Ec. Norm. Sup., 10 (1977) 419-440. Zbl0386.17004MR480653
  13. [13] A. Joseph: Kostant's problem, Goldie rank and the Gelfand-Kirillov conjecture. Invent. Math., 56 (1980) 191-213. Zbl0446.17006MR561970
  14. [14] A. Joseph: Dixmier's problem for Verma and principal series submodules. J. Lond. Math. Soc., 20 (1979) 193-204. Zbl0421.17005MR551445
  15. [15] A. Joseph: Goldie rank in the enveloping algebra of a semisimple Lie algebra. I, J. Alg., 66 (1980) 269-283. Zbl0441.17004MR585721
  16. [16] A. Joseph: Towards the Jantzen conjecture. Compos. Math., 40 (1980) 35-67. Zbl0424.17004MR558258
  17. [17] A. Joseph: Gelfand-Kirillov dimension for the annihilators of simple quotients of Verma modules. J. Lond. Math. Soc., 18 (1978) 50-60. Zbl0401.17007MR506500
  18. [18] A. Joseph and L.W. Small: An additivity principle for Goldie rank. Israel J. Math., 31 (1978) 105-114. Zbl0395.17010MR516246
  19. [19] D.A. Kazhdan and G. Lusztig: Representations of Coxeter groups and Hecke algebras. Invent. Math., 53 (1979) 165-184. Zbl0499.20035MR560412
  20. [20] J. Lepowsky: A generalization of the Bernstein-Gelfand-Gelfand resolution, J. Alg, 49 (1977) 496-511. Zbl0381.17006MR476813
  21. [21] N.N. Shapovalov: On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra. Funct. Anal. Priloz, 6 (1972) 307-311. Zbl0283.17001
  22. [22] D. Vogan: Irreducible characters of semisimple Lie groups I. Duke Math. J., 46 (1979) 61-108. Zbl0398.22021MR523602
  23. [23] D. Vogan: Irreducible characters of semisimple Lie groups II. The Kazdhan-Lusztig conjectures, preprint, M.I.T.1979. Zbl0421.22008MR552528
  24. [24] D. Vogan: Ordering in the primitive spectrum of a semisimple Lie algebra. Math. Ann., 248 (1980) 195-203. Zbl0414.17006MR575938

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