Annihilators and associated varieties of unitary highest weight modules

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1. [1] D. BARBASCH, The Unitary Dual for Complex Classical Lie Groups (Inv. Math., Vol. 96, 1989, pp. 103-176). Zbl0692.22006MR90c:22044
2. [2] D. BARBASCH and D. A. VOGAN, Primitive Ideals and Orbital Integrals in Complex Classical Groups (Math. Ann., Vol. 259, 1982, pp. 153-199). Zbl0489.22010MR83m:22026
3. [3] W. BORHO and J.-L. BRYLINSKI, Differential Operators on Homogeneous Spaces III (Invent. Math., Vol. 80, 1985, pp. 1-68). Zbl0577.22014MR87i:22045
4. [4] W. BORHO and H. KRAFT, Über die Gelfand-Kirillov Dimension (Math. Ann., Vol. 220, 1976, pp. 1-24). Zbl0306.17005MR54 #367
5. [5] N. BOURBAKI, Groupes et Algèbres de Lie, Chaps. IV-VI, Act. Sci. Ind., 1337, Hermann, Paris, 1968. MR39 #1590
6. [6] M. G. DAVIDSON, T. J. ENRIGHT and R. J. STANKE, Differential Operators and Highest Weight Representations, preprint, 1990. Zbl0759.22015
7. [7] J. DIXMIER, Algèbres enveloppantes (Cahiers scientifiques, No. 37, Gauthier-Villars, Paris, 1974). Zbl0308.17007MR58 #16803a
8. [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). Zbl0651.17003MR89m:22022
9. [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. Zbl0535.22012MR86c:22028
10. [10] T. J. ENRIGHT and A. JOSEPH, An Intrinsic Analysis of Unitarizable Highest Weight Modules (Math. Ann., Vol. 288, 1990, pp. 571-594). Zbl0725.17009MR91m:17005
11. [11] A. FREUDENTHAL, Zur eben Oktavengeometrie (Indag. Math., Vol. 15, 1953, pp. 195-200). Zbl0053.01503
12. [12] M. HARRIS and H. P. JAKOBSEN, Singular Holomorphic Representations and Singular Modular Forms (Math. Ann., Vol. 259, 1982, pp. 227-244). Zbl0466.32017MR84b:22023
13. [13] H. P. JAKOBSEN, On Singular Holomorphic Representations (Invent. Math., Vol. 62, 1980, pp. 67-78). Zbl0466.22016MR82e:22025
14. [14] H. P. JAKOBSEN, Hermitian Symmetric Spaces and Their Unitary Highest Weight Modules (J. Funct. Anal., Vol. 52, 1983, pp. 385-412). Zbl0517.22014MR85a:17004
15. [15] H. P. JAKOBSEN and M. VERGNE, Restrictions and Expansions of Holomorphic Representations (J. Funct. Anal., Vol. 34, 1979, pp. 29-53). Zbl0433.22011MR80m:22020
16. [16] J. C. JANTZEN, Einhüllenden Algebren halbeinfacher Lie-Algebren (Ergebnisse der Mathematik, Springer-Verlag, Berlin, 1983). Zbl0541.17001
17. [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). Zbl0346.17008MR53 #8168
18. [18] A. JOSEPH, A Preparation Theorem for the Prime Spectrum of a Semisimple Lie Algebra (J. Algebra, Vol. 48, 1977, pp. 241-289). Zbl0405.17007MR56 #12082
19. [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). Zbl0401.17007MR58 #22202
20. [20] A. JOSEPH, Kostant's Problem, Goldie Rank and the Gelfand-Kirillov Conjecture (Invent. Math., Vol. 56, 1980, pp. 191-213). Zbl0446.17006MR82f:17008
21. [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). Zbl0441.17004
22. [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). Zbl0374.17004MR56 #8645
23. [23] A. JOSEPH, On the Variety of a Highest Weight Module (J. Algebra, Vol. 88, 1984, pp. 238-278). Zbl0539.17006MR85j:17014
24. [24] A. JOSEPH, A Surjectivity Theorem for rigid Highest Weight Modules (Invent. Math., Vol. 92, 1988, pp. 567-596). Zbl0657.17004MR89d:17013
25. [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). Zbl0656.17009MR89k:17028
26. [26] T. LEVASSEUR and J. T. STAFFORD, Rings of Differential Operators on Classical Rings of Invariants (Mem. Am. Math. Soc., Vol. 412, 1989). Zbl0691.16019MR90i:17018
27. [27] J. C. MCCONNELL and J. C. ROBSON, Non-Commutative Noetherian Rings, Wiley-Interscience, New York, 1987. Zbl0644.16008MR89j:16023
28. [28] W. M. MCGOVERN, Quantization of Nilpotent Orbit Covers in Complex Classical Groups, preprint, 1989. 
29. [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). Zbl0585.17008MR87k:17015

1. Hans Plesner Jakobsen, An intrinsic classification of the unitarizable highest weight modules as well as their associated varieties
2. Anthony Joseph, Orbital varietes of the minimal orbit