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The\(\mathfrak{n}\)-Homology of Harish-Chandra modules: Generalizing a theorem of Kostant

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References

  1. Beilinson, A., Bernstein, J.: Localization of g-modules. C. R. Acad. Sci., Serié 1,292, 15–18 (1981)

    Google Scholar 

  2. Borho, W., Jantzen, J.: Über primative Ideale in der Einhüllenden einer halbeinfachen Lie-Algebra. Invent. Math.39, 1–53 (1977)

    Google Scholar 

  3. Brylinski, J., Kashiwara, M.: Kazhdan-Lusztig conjectures and holonomic systems. Invest. Math.64, 387–410 (1981)

    Google Scholar 

  4. Collingwood, D.: Harish-Chandra modules with the unique embedding property. Trans. Am. Math. Soc.281, 1–47 (1984)

    Google Scholar 

  5. Hecht, H.: The characters of some representations of Harish-Chandra. Math. Ann.219, 213–226 (1976)

    Google Scholar 

  6. Hecht, H., Schmid, W.: Characters, asymptotics and n-homology of Harish-Chandra modules. Acta Math.151, 49–151 (1983)

    Google Scholar 

  7. Helgason, S.: Differential geometry, Lie groups and symmetric spaces. New York: Academic Press 1978

    Google Scholar 

  8. Hiller, H.: Geometry of Coxeter groups. Research notes in Mathematics. Boston-London-Melbourne: Pitman 1982

    Google Scholar 

  9. Kazhdan, D., Lusztig, G.: Representations of Coxeter groups and Hecke algebras. Invent. Math.53, 165–184 (1979)

    Google Scholar 

  10. Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math.74, 329–387 (1961)

    Google Scholar 

  11. Parthasarathy, R.: Criteria for the unitarity of some highest weight modules. Proc. Indian Acad. Sci.89, 1–24 (1980)

    Google Scholar 

  12. Proctor, R.: Interactions between combinatories, Lie theory and algebraic geometry via the Bruhat orders. Ph. D. thesis, Massachusetts Institute of Technology, 1981.

  13. Schmid, W.: Vanishing theorems for Lie algebra cohomology and the cohomology of discrete subgroups of semisimple Lie groups. Adv. Math.41, 78–113 (1981)

    Google Scholar 

  14. Vogan, D.: Irreducible characters of semisimple Lie groups. I. Duke Math. J.46, 61–108 (1979)

    Google Scholar 

  15. Vogan, D.: Irreducible characters of semisimple Lie groups. II. The Kazhdan-Lusztig conjectures. Duke Math. J.46, 805–859 (1979)

    Google Scholar 

  16. Vogan, D.: Irreducible characters of semisimple Lie groups. III. Proof of the Kazhdan-Lusztig conjectures in the integral case. Invent. Math.71, 381–417 (1983)

    Google Scholar 

  17. Vogan, D.: Irreducible characters of semisimple Lie groups. IV. Character-multiplicity duality. Duke Math. J.49, 943–1073 (1982)

    Google Scholar 

  18. Vogan, D.: Unitarizability of certain series of representations. Ann. Math.120, 141–187 (1984)

    Google Scholar 

  19. Vogan, D.: Representations of real reductive Lie groups. Progress in Mathematics. Boston: Birkhäuser 1981

    Google Scholar 

  20. Vogan, D., Zuckerman, G.: Unitary representations with non-zero cohomology. Compos. Math.53, 51–90 (1984)

    Google Scholar 

  21. Jantzen, J.: Moduln mit einem höchsten Gewicht. Lecture Notes in Mathematics, Vol. 750. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  22. Boe, B., Collingwood, D.: A multiplicity one theorem for holomorphically induced representation. Preprint, 1984

  23. Boe, B., Collingwood, D.: Intertwining operators between holomorphically induced modules. Pac. J. Math. (to appear)

  24. Irving, R.: Projective modules in categoryO s: self duality. Trans. Am. Math. Soc. (to appear)

  25. Enright, T., Shelton, B.: Highest weight modules forU(p, q). Preprint, 1985

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Collingwood, D.H. The\(\mathfrak{n}\)-Homology of Harish-Chandra modules: Generalizing a theorem of Kostant. Math. Ann. 272, 161–187 (1985). https://doi.org/10.1007/BF01450563

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  • DOI: https://doi.org/10.1007/BF01450563

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