Pacific Journal of Mathematics

Loewy series and simple projective modules in the category ${\scr O}_S$.

Ronald S. Irving and Brad Shelton

Article information

Pacific J. Math., Volume 132, Number 2 (1988), 319-342.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B10: Representations, algebraic theory (weights)


Irving, Ronald S.; Shelton, Brad. Loewy series and simple projective modules in the category ${\scr O}_S$. Pacific J. Math. 132 (1988), no. 2, 319--342.

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  • [1] J. N. Bernstein and S. I. Gelfand, Tensor products of finite and infinite dimen- sional representationsof semisimple Lie algebras, Comp. Math., 41 (1980), 245- 285.
  • [2] D. H. Collingwood, R. S. Irving and B. Shelton, Filtrations on generalized Verma modules for Hermitian symmetric pairs, J. Reine Angew. Math., to ap- pear.
  • [3] N. Conze and J. Dixmier, Ideaux primitifs dans algebre enveloppante d'une algebrede Lie semi-simple,Bull. Soc. Math., 96 (1972), 339-351.
  • [4] T. J. Enright and B. Shelton, Categoriesof highest weight modules: applications to classicalHermitian symmetric pairs, Memoirs Amer. Math. Soc, 367 (1987).
  • [5] T. J. Enright and J. A. Wolf, Continuation of unitary derivedfunctor modules out of the canonical chamber,Mem. Soc. Math. France (N.S.), 15 (1984), 139-156.
  • [6] J. E. Humphreys, A constructionofprojective modules in the category@ of Bern- stein-Gelfand-Gelfand, Indag. Math., 39 (1977), 301-303.
  • [7] R. S. Irving, Protectivemodules in the category&\ typescript, 1982.
  • [8] R. S. Irving, Projectivemodules in the category@$\ self-duality,Trans. Amer. Math. Soc, 291 (1985), 701-732.
  • [9] R. S. Irving, Projectivemodules in the category@S'> Loewy series,Trans. Amer. Math. Soc, 291 (1985), 733-754.
  • [10] R. S. Irving, Thesocle filtration of a Verma module, preprint,1986.
  • [11] J. C.Jantzen, "Kontravariante Formen auf induzierten Darstellungenhalbein- facher Lie-algebren,Math. Ann., 226(1977),53-65.
  • [12] J.C.Jantzen, Moduln mitEinem Hchsten Gewicht, Lecture Notes inMathema- tics #750, Springer-Verlag, Berlin, Heidelbergand New York, 1979.
  • [13] A Rocha-Caridi, Splitting criteria for g-modules inducedfrom a parabolicand the Bernstein-Gelfand-Gelfand resolution of a finite-dimensional irreducible g- module, Trans. Amer. Math. Soc, 262(1980),335-366.

See also

  • Corr : Ronald S. Irving, Brad Shelton. Correction to: ``Loewy series and simple projective modules in the category ${\scr O}_S$''. Pacific Journal of Mathematics volume 135, issue 2, (1988), pp. 395-396.