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Joseph, A.

Kostant’s problem, Goldie rank and the Gelfand-Kirillov conjecture. (English) Zbl 0446.17006

Invent. Math. 56, 191-213 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0446.17006

Cited in 3 Reviews
Cited in 44 Documents

MSC:

17B35 Universal enveloping (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
16P50 Localization and associative Noetherian rings
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16Dxx Modules, bimodules and ideals in associative algebras

Keywords:

Weyl group representations; Dixmier map; Kostant problem; Goldie rank; Gelfand-Kirillov conjecture; complex semisimple Lie-algebra; enveloping algebra; primitive ideals; simple module with highest weight

Citations:

Zbl 0327.17002; Zbl 0395.17010; Zbl 0346.17014; Zbl 0441.17004
Cite Review PDF
Full Text: DOI EuDML

References:

[1] Borho, W.: Primitive vollprime Ideale in der Einhüllenden vonso (5, ?). J. Alg.43, 619-654 (1976) · Zbl 0346.17013 · doi:10.1016/0021-8693(76)90130-7
[2] Borho, W.: Definition einer Dixmier-Abbildung fürs l(n, ?). Invent. Math.,40, 143-169 (1977) · Zbl 0346.17014 · doi:10.1007/BF01390343
[3] Borho, W., Gabriel, P., Rentschler, R.: Primideale in Einhüllenden auflösbarer Lie-algebren. LN 357. Berlin, Heidelberg, New York: Springer-Verlag 1973 · Zbl 0293.17005
[4] Borho, W., Jantzen, J.C.: Über primitive Ideale in der Einhüllenden einer halbeinfacher Liealgebra. Invent. Math.39, 1-53 (1977) · doi:10.1007/BF01695950
[5] Conze, N.: Algèbres d’opérateurs différentiels et quotients des algèbres enveloppantes. Bull. Soc. Math. France,102, 379-415 (1974) · Zbl 0298.17012
[6] Conze, N., Dixmier, J.: Idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semisimple. Bull. Sci. Math.,96, 339-351 (1972) · Zbl 0246.17009
[7] Conze-Berline, N., Duflo, M.: Sur les represéntations induites des groupes semi-simples complexes. Compos. Math.,34, 307-336 (1977) · Zbl 0389.22016
[8] Dixmier, J.: Algèbres enveloppantes, cahiers scientifiques, XXXVII. Paris: Gauthier-Villars 1974
[9] Duflo, M.: Représentations irréductibles des groupes semi-simples complexes. LN497, pp. 26-88. Berlin, Heidelberg, New York: Springer-Verlag 1975
[10] Duflo, M.: Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semi-simple. Ann. Math.105, 107-130 (1977) · Zbl 0346.17011 · doi:10.2307/1971027
[11] Jantzen, J.C.: Kontravariante Formen auf induzierte Darstellungen halbeinfacher Lie-algebren. Math. Ann.226, 53-65 (1977) · Zbl 0372.17003 · doi:10.1007/BF01391218
[12] Jantzen, J.C.: Moduln mit einem höchsten Gewicht. Habilitationsschrift, Bonn 1977 · Zbl 0426.17001
[13] Joseph, A.: Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie réductive. Comptes Rendus, A284, 425-427 (1977) · Zbl 0362.17007
[14] Joseph, A.: A characteristic variety for the primitive spectrum of a semisimple Lie algebra (unpublished). Short version in LN587, pp. 102-118. Berlin, Heidelberg, New York: Springer-Verlag 1977
[15] Joseph, A.: On the annihilators of the simple subquotients of the principal series. Ann Scient. Ec. Norm. Sup. · Zbl 0386.17004
[16] Joseph, A.: A preparation theorem for the prime spectrum of a semisimple Lie algebra. J. Alg.48, 241-289 (1977) · Zbl 0405.17007 · doi:10.1016/0021-8693(77)90306-4
[17] Joseph, A.: Gelfand-Kirillov dimension for the annihilators of simple quotients of Verma modules. J. Lond. Math Soc. · Zbl 0401.17007
[18] Joseph, A.: On the Gelfand-Kirillov conjecture for induced ideals in the semisimple case. Bull. Soc. Math. France · Zbl 0407.17004
[19] Joseph, A.: Second commutant theorems in enveloping algebras. Amer. J. Math.99, 1166-1192 (1977) · Zbl 0378.17006
[20] Joseph, A.: Towards the Jantzen conjecture. Compos. Math., in press (1979) · Zbl 0424.17004
[21] Joseph, A.: Towards the Jantzen conjecture II. Compos. Math., in press (1979) · Zbl 0424.17005
[22] Joseph, A., Small, L.W.: An additivity principle for Goldie rank. Israel J. Math.31, 105-114 (1978) · Zbl 0395.17010 · doi:10.1007/BF02760541
[23] Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math.,74, 329-387 (1961) · Zbl 0134.03501 · doi:10.2307/1970237
[24] Macdonald, I.G.: Some irreducible representations of the Weyl groups. Bull. Lond. Math. Soc.,4, 148-150 (1972) · Zbl 0251.20043 · doi:10.1112/blms/4.2.148
[25] Springer, T.A.: A construction of Representations of Weyl groups. Invent. Math.,44, 279-293 (1978) · Zbl 0376.17002 · doi:10.1007/BF01403165
[26] Vogan, D.: The algebraic structure of the representations of semisimple Lie groups. Preprint, M.I.T., 1977 · Zbl 0368.20026
[27] Zuckerman, G.: Tensor products of finite and infinite dimensional representations of semisimple Lie groups. Ann. Math.,106, 215-308 (1977) · Zbl 0384.22004 · doi:10.2307/1971097
[28] Beynon, W.M., Lusztig, G.: Some numerical results on the characters of exceptional Weyl groups. Math. Proc. Camb. Phil. Soc.,84, 417-426 (1978) · Zbl 0416.20033 · doi:10.1017/S0305004100055249
[29] Joseph, A.: Dixmier’s problem for Verma and principal series submodules. J. Lond. Math. Soc., in press (1979) · Zbl 0421.17005
[30] Lusztig, G.: A class of irreducible representations of a Weyl group. Proc. Nederl. Akad., in press (1979) · Zbl 0435.20021
[31] Speh, B.: Indecomposable representations of semi-simple Lie groups. Preprint, Chicago, 1978
[32] Speh, B., Vogan, D.: Reducibility of generalized principal series representations. Preprint, M.I.T., 1978 · Zbl 0457.22011
[33] Vogan, D.: Irreducible characters of semisimple Lie groups I. Duke Math. J.,46, 61-108 (1979) · Zbl 0398.22021 · doi:10.1215/S0012-7094-79-04605-2
[34] Vogan, D.: Ordering of the primitive operation of a semisimple Lie algebra. Preprint, Princeton, 1978
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