References
Barbasch, D.: Filtrations on Verma modules. Ann Sci. Ec. Norm. Super. IV. serie16, 489–494 (1983)
Beilinson, A.: Localization of representations of reductive Lie algebras. Proc. Intern. Congr. Math., Warsaw, p. 699–710, 1983
Beilinson, A., Bernstein, J.: Localisation deg-modules. C.R. Acad. Sci. Paris, Serie I,292, 15–18 (1981)
Beilinson, A., Bernstein, J., Deligne, P.: Analyse et topologie sur les espaces singuliers I. Asterisque100, Soc. math. de france 1982
Bernstein, J.: On the Kazhdan-Lusztig conjectures. AMS summer research conference, UC Santa Cruz, July 1986
Bernstein, J., Gelfand, I., Gelfand, S.: Schubert cells and cohomology of the spacesG/P. Russ. Math. Studies28, 1–26 (1973)
Boe, B.: Homomorphsims between generalized Verma modules, Ph.D. thesis, Yale University, 1983
Boe, B., Collingwood, D.: A multiplicity one theorem for holomorphically induced representations. Math. Z.192, 265–282 (1986)
Boe, B., Collingwood, D.: Interwining operators between holomorphically induced representations. Pac. J. Math.124, 73–84 (1986)
Boe, B., Collingwood, D.: A comparison theory for the structure of induced representations. J. Algebra94, 511–545 (1985)
Boe, T., Enright, T., Shelton, B.: Interwining operators for holomorphically induced representations. Pac. J. Math. To appear
Borel, A.: Lectures on the Riemann-Hilbert correspondence. Inst. Adv. Study. Princeton, 1984–85
Brylinski, J., Kashiwara, M.: Kazhdan-Lusztig conjecture and holonomic systems. Invent. Math.64, 387–410 (1981)
Casian, L., Collingwood, D.: Complex geometry and the asymptotics of Harish-Chandra modules for real reductive Lie groups I. Trans. Am. Math. Soc.300, 73–107, 1987
Casian, L., Collingwood, D.: Complex geometry and the asymptotics of Harish-Chandra modules for real reductive Lie groups III: estimates onn-homology. J. Algebra. To appear
Casian, L., Collingwood, D.: Weight filtrations for induced representations of real reductive Lie groups. Advances in Math. To appear
Collingwood, D.: Then-homology of Harish-Chandra modules: generalizing a theorem of Kostant. Math. Ann.272, 161–187 (1985)
Collingwood, D.: Representations of rank one Lie groups. Research Notes in Mathematics 137. London: Pitman Publishing 1985
Collingwood, D., Irving, R., Shelton, B.: Filtrations on generalized Verma modules for Hermitian symmetric pairs. J. für die Reine und Angew. Math. to appear
Deodhar, V.: On some geometric aspects for Bruhat orderings II: The parabolic analogue of Kazhdan-Lusztig polynomials. J Algebra, to appear
Dixmier, J.: Enveloping Algebras. Amsterdam: North-Holland 1977
Enright, T., Shelton, B.: Categories of highest weight modules: applications to classical Hermitian symmetric pairs. Memoirs of the AMS. To appear
Gelfand, I., MacPherson, R.: Verma modules and Schubert cells: a dictionary. Springer Lecture Notes924, 1–50 (1982)
Hecht, H., Miličić, D., Schmid, W., Wolf, J.: Localisation and standard modules for real semisimple Lie groups I: the duality theorem. Preprint 1986
Helgason, S.: Differential geometry. Lie groups and symmetric spaces. New York: Academic Press 1978
Hiller, S.: Geometry of Coxeter groups. Research Notes in Mathematics 54. London: Pitman Publishing 1982
Irving, R.: Projective modules in categoryO s : self duality. Trans. Am. Math. Soc.291, 701–732 (1985)
Jakobsen, H.: Basic covariant differential operators on Hermitian symmetric spaces. Ann. Ecol. Norm. Sup. To appear
Kazhdan, D., Lusztig, G.: Representations of Coxeter groups and Hecke algebras. Invent. Math.53, 165–184 (1979)
Kazhdan, D., Lusztig, G.: Schubert varieties and Poincare duality. Proc. Symp. Pure Math.36, 185–203 (1980)
Lepowsky, J.: A generalization of the Bernstein-Gelfand-Gelfand resolution. J. Algebra49, 496–511 (1977)
Lusztig, G., Vogan, D.: Singularities of closures ofK-orbits on flag manifold. Invent. Math.71, 365–370 (1983)
Milicic, D.: Classification of Harish-Chandra modules. Lecture at the Inst. Adv. Study, Princeton, Oct. 22, 1985
Vogan, D.: Irreducible characters of semisimple Lie groups III: Proof of the Kazhdan-Lusztig conjecture in the integral case. Invent. Math.71, 381–417 (1983)
Vogan, D.: Complex geometry and representations of reductive groups. Manuscript
Casian, L.: The socle filtration of an induced representation with a unique irreducible submodule. Preprint, 1987
Beilinson, A., Ginsberg, V.: Mixed categories, Ext-duality and representations. Preprint, 1987
Irving, R., Shelton, B.: Loewy series and simple projective modules inO s . Pac. J. Math. To appear
Irving, R.: The socle filtration of a Verma module. Preprint, 1987
Irving, R.: BGG algebras. In preparation
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Supported by an NSF Postdoctoral Fellowship MCS 85-11467
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Casian, L.G., Collingwood, D.H. The Kazhdan-Lusztig conjecture for generalized Verma modules. Math Z 195, 581–600 (1987). https://doi.org/10.1007/BF01166705
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DOI: https://doi.org/10.1007/BF01166705