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Differential operators on homogeneous spaces. I: Irreducibility of the associated variety for annihilators of induced modules. (English) Zbl 0504.22015

MSC:
22E60 Lie algebras of Lie groups
53C30 Differential geometry of homogeneous manifolds
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
22E30 Analysis on real and complex Lie groups
17B35 Universal enveloping (super)algebras
17B20 Simple, semisimple, reductive (super)algebras
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[1] [AMa] Abraham, R., Marsden, J.E.: Foundations of mechanics, 2. edition. Benjamin/Cummings Publ. Co., Reading, Ma. 1978
[2] [Al] Alekse’evski, A.V.: Component groups of centralizer for unipotent elements in semisimple algebraic groups (in Russian). Trudy Tbilisskogo Matematicheskogo Instituta62, 5-28 (1979)
[3] [Av] Alvis, D.: Induce/restrict matrices for exceptional Weyl groups. Manuscript, M.I.T., Cambridge, MA, 1981
[4] [AvL] Alvis, D., Lusztig, G.: On Springer’s correspondence for simple groups. Preprint, M.I.T., Cambridge, MA, 1981
[5] [BaV1] Barbasch, D., Vogan, D.: Primitive ideals and orbital integrals in complex classical groups. Math. Ann.259, 153-199 (1982) · Zbl 0489.22010
[6] [BaV2] Barbasch, D., Vogan, D.: Primitive ideals and orbital integrals in complex exceptional groups. Preprint, M.I.T. 1981 · Zbl 0513.22009
[7] [BaV3] Barbasch, D., Vogan, D.: The local structure of characters. J. of Functional Analysis37, 27-55 (1980) · Zbl 0436.22011
[8] [BeBe] Beilinson, A., Bernstein, J.: Localisation de g-modules. C. R. Acad. Sc. Paris292, 15-18 (1981) · Zbl 0476.14019
[9] [Be] Bernstein, I.N.: Modules over a ring of differential operators. Study of the fundamental solutions of equations with constant coefficients. Funct. Anal. Apl.5, 98-101 (1971) · Zbl 0233.47031
[10] [Bj] Björk, J.-E.: Rings of differential operators. North-Holland Pub. Co., Amsterdam-New York-Oxford 1979 · Zbl 0198.35903
[11] [B1] Borho, W.: Berechnung der Gelfand-Kirillov-Dimension bei induzierten Darstellungen. Math. Ann.225, 177-194 (1977) · Zbl 0346.17012
[12] [B2] Borho, W.: Recent advances in enveloping algebras of semi-simple Lie-algebras. Sémin. Bourbaki, Exposé 489 (1976); Lecture Notes in Math., vol.677. Berlin-Heidelberg-New York. Springer 1978
[13] [B3] Borho, W.: Definition einer Dixmier-Abbildung für \(\mathfrak{s}\mathfrak{l}(n,\mathbb{C})\) . Invent. Math.40, 143-169 (1977) · Zbl 0346.17014
[14] [B4] Borho, W.: Über Schichten halbeinfacher Lie-Algebren; Invent. Math.65, 283-317 (1981) · Zbl 0484.17004
[15] [BJ] Borho, W., Jantzen, J.-C.: Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie-Algebra. Invent. Math.39, 1-53 (1977) · Zbl 0339.17006
[16] [BK1] Borho, W., Kraft, H.: Über die Gelfand-Kirillov-Dimension. Math. Ann.220, 1-24 (1976) · Zbl 0313.17004
[17] [BK2] Borho, W., Kraft, H.: Über Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen. Comment. Math. Helvet.54, 61-104 (1979) · Zbl 0395.14013
[18] [BM1] Borho, W., MacPherson, R.: Représentations des groupes de Weyl et homologie d’intersection pour les variétés nilpotentes. Note C.R.A.S. Paris t.29 (27 april 1981). pp. 707-710 · Zbl 0467.20036
[19] [BM2] Borho, W., MacPherson, R.: Partial resolutions of nilpotent varieties; Proceedings of the conference on ?Analyse et Topologie sur les variétés singulières?, organized by Teissier and Verdier at Marseille-Luminy 1981 (to appear in Astérisque)
[20] [Br] Brylinski, J.-L.: Differential Operators on the Flag Varieties; Proceedings of the Conference on ?Young tableaux and Schur functors in Algebra and Geometry? at Torun (Poland) 1980 (to appear)
[21] [BrKa] Brylinski, J.-L., Kashiwara, M.: Kazhdan-Lusztig conjecture and holonomic systems. Invent. math.64, 387-410 (1981) · Zbl 0473.22009
[22] [CD] Conze-Berline, N., Duflo, M.: Sur les repr?entations induites des groupes semi-simples complexes. Compositio math.34, 307-336 (1977) · Zbl 0389.22016
[23] [Di] Dixmier, J.: Algèbres enveloppantes. Paris: Gauthier-Villars 1974
[24] [D] Duflo, M.: Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semisimple. Annals of Math.105, 107-120 (1977) · Zbl 0346.17011
[25] [EGA] Dieudonné, J., Grothendieck, A.: Eléments des Géométrie Algébrique III (Étude cohomologique des faisceaux cohérentes): Publ. Math. IHES n0 11 (1961) and n0 17 (1963)
[26] [EP] Elashvili, A.G., Panov, A.N.: Polarizations in semisimple Lie-algebras (in Russian). Bull. Acad. Sci. Georgian SSR87, 25-28 (1977) · Zbl 0368.17005
[27] [E1] Elkik, R.: Désingularisation des adhérences d’orbites polarisables et des nappes dans les algèbres de Lie réductives. Preprint, Paris 1978
[28] [GKi] Gelfand, I.M., Kirillov, A.A.: The structure of the Lie field connected with a split semisimple Lie algebra. Funct. Anal. Applic.3, 6-21 (1969) · Zbl 0244.17007
[29] [Gi] Ginsburg, V.: Symplectic geometry and representations. Preprint, Moscow State University, 1981
[30] [Ha] Hartshorne, R.: Residues and duality. Lecture Notes in Math., Vol. 20. Berlin-Heidelberg-New York: Springer 1966 · Zbl 0212.26101
[31] [He] Hesselink, W.H.: Polarization in the classical groups. Math. Z.160, 217-234 (1978) · Zbl 0372.20030
[32] [HS] Hotta, R., Springer, T.A.: A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups. Invent. math.41, 113-127 (1977) · Zbl 0389.20037
[33] [H] Hotta, R.: The Weyl groups as monodromies and nilpotent orbits (after M. Kashiwara); preprint, Tohoku University, 1982
[34] [J] Jantzen, J.-C.: Moduln mit einem höchsten Gewicht; Lecture Notes in Math., vol. 750. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0426.17001
[35] [Ja] Jategaonkar, A.V.: Solvable Lie algebras, polycyclic-by-finite groups, and bimodule Krull dimension. Communications in Algebra10, 19-69 (1982) · Zbl 0476.16014
[36] [Jo1] Joseph, A.: Towards the Jantzen conjecture I, II. Compositio math.40, 35-67, 69-78 (1980)
[37] [Jo2] Joseph, A.: Towards the Jantzen conjecture III. Compositio math.41, 23-30 (1981)
[38] [Jo3] Joseph, A.: Kostant’s problem, Goldie-rank, and the Gelfand-Kirillov conjecture. Invent. math.56, 191-213 (1980) · Zbl 0446.17006
[39] [Jo4] Joseph, A.: Goldie rank in the enveloping algebra of a semisimple Lie algebra I, II. J. of Algebra65, 269-306 (1980) · Zbl 0441.17004
[40] [Jo5] Joseph, A.:W-module structure in the primitive spectrum of the enveloping algebra of a semisimple Lie algebra. In: Noncommutative Harmonic Analysis, Lecture Notes in Mathematics, vol. 728, pp. 116-135. Berlin-Heidelberg-New York: Springer 1978
[41] [KKS] Kazhdan, D., Kostant, B., Sternberg, S.: Hamitonian group actions and dynamical systems of Calogero type. Commun. Pure Appl. Math.31, 481-507 (1978) · Zbl 0368.58008
[42] [Ke1] Kempf, G.: The Grothendieck Cousin complex of an induced representation. Advances in Math.29, 310-396 (1978) · Zbl 0393.20027
[43] [Ke2] Kempf, G.: The geometry of homogeneous spaces versus induced representations. In: Supplement. American J. Math.: Algebraic Geometry, J.-I. Igusa ed., The Johns Hopkins centen. Lect., Symp. Baltimore/Maryland 1976, 1-5 (1977)
[44] [Kk] Kempken, G.: Induced conjugacy classes in classical Lie-algebras. Abh. Math. Sem. Univ. Hamburg (to appear) · Zbl 0495.17003
[45] [Ko1] Kostant, B.: Quantization and unitary representation. In: Lectures in Modern Analysis and Applications III. Lecture Notes in Mathematics, vol. 170, pp. 87-208, Berlin-Heidelberg-New York: Springer 1976
[46] [Ko2] Kostant, B.: Quantization and representation theory; In: Representation Theory of Lie Groups. Proceedings, London Math. Soc. Lecture Notes Series34, 287-316 (1979)
[47] [KP1] Kraft, H., Procesi, C.: Closures of Conjugacy Classes of Matrices are Normal. Invent. math.53, 227-247 (1979) · Zbl 0434.14026
[48] [KP2] Kraft, H., Procesi, C.: On the geometry of conjugacy classes in classical groups. Comment. Math. Helvet. (to appear) · Zbl 0511.14023
[49] [L] Lusztig, G.: A class of irreducible representations of a Weyl group. Proc. Kon. Nederl. Akad. Wetensch.82, 323-335 (1979) · Zbl 0435.20021
[50] [Md] Macdonald, I.G.: Some irreducible representations of Weyl groups. Bull. London Math. Soc.4, 148-150 (1972) · Zbl 0251.20043
[51] [Mi] Mizuno, K.: The conjugate classes of unipotent elements of the Chevalley groupsE 7 andE 8. Tokyo J. Math.3, 391-459 (1980) · Zbl 0454.20046
[52] [Mü] Müller, B.J.: Localizations in non-commutative noetherian rings. Can. J. Math.28, 600-610 (1976) · Zbl 0344.16004
[53] [R] Richardson, R.-W.: Conjugacy classes in parabolic subgroups of semi-simple algebraic groups. Bull. London Math. Soc.6, 21-24 (1974) · Zbl 0287.20036
[54] [?] ?apovalov, N.N.: On a conjecture of Gel’fand-Kirillov. Funct. Anal. Applic.7, 165-166 (1973) · Zbl 0291.22011
[55] [Sh] Shoji, T.: The conjgacy classes of Chevalley groups of type (F 4) over finite fields of characteristicp?2. J. Fac. Sci. Univ. Tokyo21, 1-17 (1974)
[56] [So] Souriau, J.M.: Structure des systèmes dynamiques. Paris: Dunod 1970 · Zbl 0186.58001
[57] [Sp] Spaltenstein, N.: The fixed point set of a unipotent transformation on the flag manifold. Proc. Kon. Nederl. Akad. Wetensch.79, 452-456 (1976) · Zbl 0343.20029
[58] [Sp2] Spaltenstein, N.: A property of special representions of Weyl groups; preprint, Warwick 1982
[59] [S1] Springer, T.A.: The unipotent variety of a semisimple group. Proc. Colloqu. Alg. Geom. Tata Inst., Bombay 1968, 373-391 (1969)
[60] [S2] Springer, T.A.: Trigonometric sums, Green functions of finite groups and representations of Weyl groups. Invent. math.36, 173-207 (1976) · Zbl 0374.20054
[61] [S3] Springer, T.A.: A construction of representations of Weyl groups. Invent. math.44, 279-293 (1978) · Zbl 0376.17002
[62] [SXt] Steinberg, R.: Conjugacy classes in algebraic groups. Lecture Notes in Mathematics, vol. 366. Berlin-Heidelberg-New York: Springer 1974
[63] [W] Wallach, N.: On the Enright-Varadarajan modules. A construction of the discrete series. Ann. Sci. Ec. Norm. Sup. 4e, sér.9, 81-102 (1976) · Zbl 0379.22008
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