Annihilators and associated varieties of unitary highest weight modules
Joseph, Anthony
Annales scientifiques de l'École Normale Supérieure, Tome 25 (1992), p. 1-45 / Harvested from Numdam
@article{ASENS_1992_4_25_1_1_0,
     author = {Joseph, Anthony},
     title = {Annihilators and associated varieties of unitary highest weight modules},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {25},
     year = {1992},
     pages = {1-45},
     doi = {10.24033/asens.1642},
     mrnumber = {93e:17010},
     zbl = {0752.17007},
     mrnumber = {1152612},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1992_4_25_1_1_0}
}
Joseph, Anthony. Annihilators and associated varieties of unitary highest weight modules. Annales scientifiques de l'École Normale Supérieure, Tome 25 (1992) pp. 1-45. doi : 10.24033/asens.1642. http://gdmltest.u-ga.fr/item/ASENS_1992_4_25_1_1_0/

[1] D. Barbasch, The Unitary Dual for Complex Classical Lie Groups (Inv. Math., Vol. 96, 1989, pp. 103-176). | MR 90c:22044 | Zbl 0692.22006

[2] D. Barbasch and D. A. Vogan, Primitive Ideals and Orbital Integrals in Complex Classical Groups (Math. Ann., Vol. 259, 1982, pp. 153-199). | MR 83m:22026 | Zbl 0489.22010

[3] W. Borho and J.-L. Brylinski, Differential Operators on Homogeneous Spaces III (Invent. Math., Vol. 80, 1985, pp. 1-68). | MR 87i:22045 | Zbl 0577.22014

[4] W. Borho and H. Kraft, Über die Gelfand-Kirillov Dimension (Math. Ann., Vol. 220, 1976, pp. 1-24). | MR 54 #367 | Zbl 0306.17005

[5] N. Bourbaki, Groupes et Algèbres de Lie, Chaps. IV-VI, Act. Sci. Ind., 1337, Hermann, Paris, 1968. | MR 39 #1590

[6] M. G. Davidson, T. J. Enright and R. J. Stanke, Differential Operators and Highest Weight Representations, preprint, 1990.

[7] J. Dixmier, Algèbres enveloppantes (Cahiers scientifiques, No. 37, Gauthier-Villars, Paris, 1974). | MR 58 #16803a | Zbl 0308.17007

[8] T. J. Enright, Analogues of Kostant's u Cohomology Formulas for Unitary Highest Weight Modules (J. reine angew. Math., Vol. 392, 1988, pp. 27-36). | MR 89m:22022 | Zbl 0651.17003

[9] T. J. Enright, R. Howe and N. R. Wallach, A Classification of Unitary Highest Weight Modules, in Representation Theory of Reductive Groups, P. C. Trombi Ed., Boston, 1983, pp. 97-143. | MR 86c:22028 | Zbl 0535.22012

[10] T. J. Enright and A. Joseph, An Intrinsic Analysis of Unitarizable Highest Weight Modules (Math. Ann., Vol. 288, 1990, pp. 571-594). | MR 91m:17005 | Zbl 0725.17009

[11] A. Freudenthal, Zur eben Oktavengeometrie (Indag. Math., Vol. 15, 1953, pp. 195-200). | Zbl 0053.01503

[12] M. Harris and H. P. Jakobsen, Singular Holomorphic Representations and Singular Modular Forms (Math. Ann., Vol. 259, 1982, pp. 227-244). | MR 84b:22023 | Zbl 0466.32017

[13] H. P. Jakobsen, On Singular Holomorphic Representations (Invent. Math., Vol. 62, 1980, pp. 67-78). | MR 82e:22025 | Zbl 0466.22016

[14] H. P. Jakobsen, Hermitian Symmetric Spaces and Their Unitary Highest Weight Modules (J. Funct. Anal., Vol. 52, 1983, pp. 385-412). | MR 85a:17004 | Zbl 0517.22014

[15] H. P. Jakobsen and M. Vergne, Restrictions and Expansions of Holomorphic Representations (J. Funct. Anal., Vol. 34, 1979, pp. 29-53). | MR 80m:22020 | Zbl 0433.22011

[16] J. C. Jantzen, Einhüllenden Algebren halbeinfacher Lie-Algebren (Ergebnisse der Mathematik, Springer-Verlag, Berlin, 1983). | Zbl 0541.17001

[17] A. Joseph, The Minimal Orbit in a Simple Lie Algebra and Its Associated Maximal Ideal (Ann. Ec. Norm. Sup., Vol. 9, 1976, pp. 1-30). | Numdam | MR 53 #8168 | Zbl 0346.17008

[18] A. Joseph, A Preparation Theorem for the Prime Spectrum of a Semisimple Lie Algebra (J. Algebra, Vol. 48, 1977, pp. 241-289). | MR 56 #12082 | Zbl 0405.17007

[19] A. Joseph, Gelfand-Kirillov Dimension for the Annihilators of Simple Quotients of Verma Modules (J. Lond. Math. Soc., Vol. 18, 1978, pp. 50-60). | MR 58 #22202 | Zbl 0401.17007

[20] A. Joseph, Kostant's Problem, Goldie Rank and the Gelfand-Kirillov Conjecture (Invent. Math., Vol. 56, 1980, pp. 191-213). | MR 82f:17008 | Zbl 0446.17006

[21] A. Joseph, Goldie Rank in the Enveloping Algebra of a Semisimple Lie Algebra I-III (J. Algebra, Vol. 65, 1980, pp. 269-283 and 284-306, Vol. 73, 1981, pp. 295-326). | Zbl 0441.17004

[22] A. Joseph, A Characteristic Variety for the Primitive Spectrum of a Semisimple Lie Algebra, in Non-Commutative Harmonic Analysis (Lectures Notes, No. 587, Berlin, 1977, pp. 102-118). | MR 56 #8645 | Zbl 0374.17004

[23] A. Joseph, On the Variety of a Highest Weight Module (J. Algebra, Vol. 88, 1984, pp. 238-278). | MR 85j:17014 | Zbl 0539.17006

[24] A. Joseph, A Surjectivity Theorem for rigid Highest Weight Modules (Invent. Math., Vol. 92, 1988, pp. 567-596). | MR 89d:17013 | Zbl 0657.17004

[25] T. Levasseur, S. P. Smith and J. T. Stafford, The Minimal Nilpotent Orbit, the Joseph Ideal and Differential Operators (J. Algebra, Vol. 116, 1988, pp. 480-501). | MR 89k:17028 | Zbl 0656.17009

[26] T. Levasseur and J. T. Stafford, Rings of Differential Operators on Classical Rings of Invariants (Mem. Am. Math. Soc., Vol. 412, 1989). | MR 90i:17018 | Zbl 0691.16019

[27] J. C. Mcconnell and J. C. Robson, Non-Commutative Noetherian Rings, Wiley-Interscience, New York, 1987. | MR 89j:16023 | Zbl 0644.16008

[28] W. M. Mcgovern, Quantization of Nilpotent Orbit Covers in Complex Classical Groups, preprint, 1989.

[29] D. A. Vogan, The Orbit Method and Primitive Ideals for Semisimple Lie Algebras, (Canad. Math. Soc. Conference Proceedings, Vol. 5, 1986, pp. 281-316). | MR 87k:17015 | Zbl 0585.17008