On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula
Gabber, O. ; Joseph, A.
Compositio Mathematica, Tome 44 (1981), p. 107-131 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{CM_1981__43_1_107_0,
     author = {Gabber, Ofer and Joseph, Anthony},
     title = {On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula},
     journal = {Compositio Mathematica},
     volume = {44},
     year = {1981},
     pages = {107-131},
     mrnumber = {631430},
     zbl = {0461.17004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1981__43_1_107_0}
}

Gabber, O.; Joseph, A. On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula. Compositio Mathematica, Tome 44 (1981) pp. 107-131. http://gdmltest.u-ga.fr/item/CM_1981__43_1_107_0/

[1] I.N. Bernstein, I.M. Gelfand and S.I. Gelfand: Category of g modules, Funct. Anal. Priloz., 10 (1976) 1-18. | Zbl 0353.18013

[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.]. | Zbl 0338.58019

[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. | Numdam | MR 581584 | Zbl 0445.17006

[4] W. Borho and J.C. Jantzen: Über primitive Ideale in der Einhüllenden einer halbeinfacher Lie-Algebra. Invent. Math., 39 (1977) 1-53. | MR 453826 | Zbl 0327.17002

[5] N. Conze-Berline and M. Duflo: Sur les représentations induites des groupes semi-simples complexes. Compos. Math., 34 (1977) 307-336. | Numdam | MR 439991 | Zbl 0389.22016

[6] P. Delorme: Extensions dans la cátegorie O de Bernstein-Gelfand-Gelfand. Applications, preprint, Paris, 1977.

[7] J. Dixmier: Algèbres enveloppantes. Cahiers scientifiques, XXXVII, Gauthier-Villars, Paris, 1974. | MR 498737 | Zbl 0308.17007

[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. | MR 430005 | Zbl 0346.17011

[9] M. Duflo: Representations irréductibles des groupes semi-simples complexes, in LN 497, Springer-Verlag, Berlin/ Heidelberg/New York, 1975, pp. 26-88. | MR 399353 | Zbl 0315.22008

[10] O. Gabber and A. Joseph: Towards the Kazhdan-Lusztig conjecture. Ann. Ec. Norm. Sup. (in the press). | Numdam | Zbl 0476.17005

[11] J.C. Jantzen: Moduln mit einem höchten Gewicht, LN 750, Springer-Verlag, Berlin/Heidelberg /New York, 1979. | MR 552943 | Zbl 0426.17001

[12] A. Joseph: On the annihilators of the simple subquotients of the principal series. Ann. Ec. Norm. Sup., 10 (1977) 419-440. | Numdam | MR 480653 | Zbl 0386.17004

[13] A. Joseph: Kostant's problem, Goldie rank and the Gelfand-Kirillov conjecture. Invent. Math., 56 (1980) 191-213. | MR 561970 | Zbl 0446.17006

[14] A. Joseph: Dixmier's problem for Verma and principal series submodules. J. Lond. Math. Soc., 20 (1979) 193-204. | MR 551445 | Zbl 0421.17005

[15] A. Joseph: Goldie rank in the enveloping algebra of a semisimple Lie algebra. I, J. Alg., 66 (1980) 269-283. | MR 585721 | Zbl 0441.17004

[16] A. Joseph: Towards the Jantzen conjecture. Compos. Math., 40 (1980) 35-67. | Numdam | MR 558258 | Zbl 0424.17004

[17] A. Joseph: Gelfand-Kirillov dimension for the annihilators of simple quotients of Verma modules. J. Lond. Math. Soc., 18 (1978) 50-60. | MR 506500 | Zbl 0401.17007

[18] A. Joseph and L.W. Small: An additivity principle for Goldie rank. Israel J. Math., 31 (1978) 105-114. | MR 516246 | Zbl 0395.17010

[19] D.A. Kazhdan and G. Lusztig: Representations of Coxeter groups and Hecke algebras. Invent. Math., 53 (1979) 165-184. | MR 560412 | Zbl 0499.20035

[20] J. Lepowsky: A generalization of the Bernstein-Gelfand-Gelfand resolution, J. Alg, 49 (1977) 496-511. | MR 476813 | Zbl 0381.17006

[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. | Zbl 0283.17001

[22] D. Vogan: Irreducible characters of semisimple Lie groups I. Duke Math. J., 46 (1979) 61-108. | MR 523602 | Zbl 0398.22021

[23] D. Vogan: Irreducible characters of semisimple Lie groups II. The Kazdhan-Lusztig conjectures, preprint, M.I.T. 1979. | MR 552528 | Zbl 0421.22008

[24] D. Vogan: Ordering in the primitive spectrum of a semisimple Lie algebra. Math. Ann., 248 (1980) 195-203. | MR 575938 | Zbl 0414.17006