The primitive spectrum of an enveloping algebra

Joseph, Anthony

Orbites unipotentes et représentations III. Orbites et faisceaux pervers, Astérisque, no. 173-174 (1989), pp. 13-53.

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     author = {Joseph, Anthony},
     title = {The primitive spectrum of an enveloping algebra},
     booktitle = {Orbites unipotentes et repr\'esentations III. Orbites et faisceaux pervers},
     series = {Ast\'erisque},
     pages = {13--53},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {173-174},
     year = {1989},
     mrnumber = {1021509},
     zbl = {0714.17011},
     language = {en},
     url = {http://www.numdam.org/item/AST_1989__173-174__13_0/}
}

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Joseph, Anthony. The primitive spectrum of an enveloping algebra, dans Orbites unipotentes et représentations III. Orbites et faisceaux pervers, Astérisque, no. 173-174 (1989), pp. 13-53. http://www.numdam.org/item/AST_1989__173-174__13_0/

Bibliographie
Cité par

[1]. D. Barbasch and D. Vogan, Primitive ideals and orbital integrals in complex classical groups, Math. Ann. 259 (1982), 152-199. | DOI | EuDML | MR | Zbl

[2]. D. Barbasch and D. Vogan, Primitive ideals and orbital integrals in complex exceptional groups, J. Algebra 80 (1983), 350-382. | DOI | MR | Zbl

[3]. A. A. Beilinson and I. N. Bernstein, Localization of $\underset{̲}{g}$ modules, C.R. Acad. Sci. Paris Sér A, 292 (1981), 15-18. | MR | Zbl

[4]. I. N. Bernstein and S. I. Gelfand, Tensor products of finite and infinite dimensional representations of semi-simple Lie algebras, Compos. Math. 41 (1980), 245-285. | EuDML | Numdam | MR | Zbl

[5]. W. Borho, P. Gabriel and R. Rentschler, Primideale in Einhüllenden auflösbarer Lie-Algebren, Lecture Notes in Mathematics 357 (Springer, Berlin, 1973). | MR | Zbl

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

[7]. J. L. Brylinski and M. Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), 387-410. | DOI | EuDML | MR | Zbl

[8]. J. Dixmier, Sur les algèbres de Weyl, Bull. Soc. Math. France, 96 (1968), 209-242. | DOI | EuDML | Numdam | MR | Zbl

[9]. J. Dixmier, Enveloping algebras, (North-Holland, New York, 1977). | MR

[10]. I. N. Herstein, Topics in Ring theory, (The University of Chicago Press, Chicago, 1969). | MR | Zbl

[11]. R. S. Irving, The socle filtration of a Verma module, Ann. Ec. Norm. Sup. (to appear). | EuDML | Numdam | MR | Zbl

[12]. J. C. Jantzen, Einhüllenden Algebren halbeinfacher Lie-Algebren, Ergebnisse der Mathematik (Springer, Berlin, 1983). | MR | Zbl

[13]. A. Joseph, Dixmier's problem for Verma and principal series modules, J. Lond. Math. Soc. 20 (1979), 193-204. | DOI | MR | Zbl

[14]. A. Joseph, $W$ -module structure in the primitive spectrum of the enveloping algebra of a semisimple Lie algebra, in Lecture Notes in Mathematics 728, pp. 116-135 (Springer, Berlin, 1979). | MR | Zbl

[15]. A. Joseph, Goldie rank in the enveloping algebra of a semisimple Lie algebra I, J. Algebra, 66 (1980), 269-283, 284-306 ; | DOI | MR | Zbl

A. Joseph, Goldie rank in the enveloping algebra of a semisimple Lie algebra II, III, J. Algebra, 73 (1981), 295-326. | DOI | MR | Zbl

[16]. A. Joseph, On the variety of a highest weight module, J. Algebra 88 (1984), 238-278. | DOI | MR | Zbl

[17]. A. Joseph, The Enright functor in the Bernstein-Gelfand-Gelfand $𝒪$ category, Invent. Math. 67 (1982), 423-445. | DOI | EuDML | MR | Zbl

[18]. A. Joseph, Completion functors in the $𝒪$ category, in Lecture Notes in mathematics, 1020, pp. (Springer, Berlin, 1983). | MR | Zbl

[19]. A. Joseph, On the cyclicity of vectors associated with Duflo involutions, in Lecture Notes in mathematics, 1243, pp. 144-188 (Springer, Berlin, 1987). | MR | Zbl

[20]. A. Joseph, A sum rule for scale factors in the Goldie rank polynomials, J. Algebra (to appear). | MR | Zbl

[21]. A. Joseph, Primitive ideals in enveloping algebras, ICM proceedings pp. 403-414 (Polish Scientific Publishers - North Holland, Warsaw, 1984). | MR | Zbl

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

[23]. G. B. Krause and T. H. Lenagen, Growth of algebras and Gelfand-Kirillov dimension, Research Notes in mathematics, 116 (Pitman, London, 1985). | MR | Zbl

[24]. G. Lusztig, Cells in affine Weyl groups II, J. of Algebra, 109 (1987), 536-548. | DOI | MR | Zbl

[25]. G. Lusztig, Leading coefficients of character values of Hecke algebras, Proceedings of Symposia in Pure Mathematics 47 American Math. Soc. (1987), 235-262. | DOI | MR | Zbl

[26]. C. Moeglin, Idéaux primitifs dans les algebres enveloppantes, J. Math, pures et appl. 59 (1980), 265-336. | MR | Zbl

[27]. C. Moeglin and R. Rentschler, Sur la classification des idéaux primitifs des algebres enveloppantes, Bull. Soc. Math. France, 112 (1984). | EuDML | Numdam | MR | Zbl

[28]. W. Soergel, Equivalences de certains catégories de $\underset{̲}{g}$ modules, C.R. Acad. Sci. Série I, 303 (1986), 725-728. | MR | Zbl

[29]. D. Vogan, Ordering of the primitive spectrum of a semisimple Lie algebra, Math. Ann. 248 (1980), 195-203. | DOI | EuDML | MR | Zbl

[30]. D. Vogan, The orbit method and primitive ideals for semisimple Lie algebras, Canadian Math. Soc. Conference Proceedings, Vol. 5 (1986), 281-316. | MR | Zbl

[31.] D. Barbasch and D. Vogan, Unipotent representations of complex semisimple groups, Ann. Math. 121 (1985), 41-110. | DOI | MR | Zbl

[32.] I. N. Bernstein, I. M. Gelfand and S. Gelfand, The structure of representations generated by vectors of largest weight, Functional analysis and its applications, 5 (1971), 1-19. | DOI | MR | Zbl

[33] I. N. Bernstein, I. M. Gelfand and S. Gelfand, Differential operators on the base affine space and a study of $\underset{̲}{g}$ modules, in : I.M. Gelfand, ed., Publ. of 1971 Summer School in Math. Janos Bolyai Math. Soc., Budapest, 21-64. | MR | Zbl

[34] N. Conze, Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes, Bull. Soc. Math. France, 102 (1974), 379-415. | DOI | EuDML | Numdam | MR | Zbl

[35] M. Duflo, Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple, Ann. Math. 105 (1977), 107-130. | DOI | MR | Zbl

[36] G. Lusztig, Characters of a reductive group over a finite field, Ann. of Math. Studies 107, Princeton Univ. Press, 1984. | MR | Zbl

[37] R. Rentschler, Primitive ideals in enveloping algebras (General Case), in Noetherian rings and their applications (Oberwolfach 1983), Math. Surveys Monographs, 24, Amer. Math. Soc., Providence, R.I. (1987), 37-57. | DOI | MR | Zbl

[38] N. Spaltenstein, Classes Unipotentes et Sous-groupes de Borel, Lecture Notes in Mathematics, 946 Springer-Verlag, Berlin 1982. | MR | Zbl

[39.] D. Vogan, Gelfand-Kirillov dimension for Harish-Chandra modules, Inv. Math. 48 (1978), 75-98. | DOI | EuDML | MR | Zbl