Keywords
- Weight Module
- Discrete Series
- Composition Factor
- Verma Module
- Bruhat Order
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
I. N. Bernštein, I. M. Gelfand, S. I. Gelfand, The structure of representations generated by vectors of highest weight, Functional Anal. Appl. 5 (1971), 1–9.
_____, Differential operators on the base affine space and a study of g-modules, pp. 21–64, Lie Groups and their Representations, Halsted, New York, 1975.
_____, A category of g-modules, Functional Anal. Appl. 10 (1976), 87–92.
P. Delorme, Extensions dans la categorie 0 de Bernštein-Gelfand-Gelfand, Applications. (preprint).
V. V. Deodhar, Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function, Invent. Math. 39 (1977), 187–198.
_____, On a construction of representations and a problem of Enright (preprint).
J. Dixmier, Algèbres Enveloppantes, Gauthier-Villars, Paris, 1974; English translation, North-Holland, Amsterdam, 1977.
T. J. Enright, On the algebraic construction and classification of Harish-Chandra modules, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), 1063–1065.
_____, On the fundamental series of a real semisimple Lie algebra: their irreducibility, resolutions and multiplicity formulae, Ann. of Math. 110 (1979), 1–82.
_____, The representations of complex semisimple Lie groups (preprint).
T. J. Enright, V. S. Varadarajan, On an infinitesimal characterization of the discrete series, Ann. of Math. 102 (1975), 1–15.
H. Garland, J. Lepowsky, Lie algebra homology and the Macdonald-Kac formulas, Invent. Math. 34 (1976), 37–76.
H. Hecht, W. Schmid, A proof of Blattner's conjecture, Invent. Math. 31 (1975), 129–154.
J. E. Humphreys, Finite and infinite dimensional modules for semisimple Lie algebras, pp. 1–64, Queen's Papers in Pure & Appl. Math. No. 48, Kingston, Ont., 1978.
J. C. Jantzen, Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren, Math. Ann. 226 (1977), 53–65.
_____, Moduln mit einem höchsten Gewicht, Habilitationsschrift, U. Bonn, 1977, to appear in Lect. Notes in Math.750, Springer, 1979.
A. Joseph, Dixmier's problem for Verma and principal series submodules, J. London Math. Soc. 20(1979), 193–204.
D. Kazhdan, G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165–184.
J. Lepowsky, A generalization of the Bernštein-Gelfand-Gelfand resolution, J. Algebra 49 (1977), 496–511.
A. Rocha-Caridi, Splitting criteria for g-modules induced from a parabolic and the Bernštein-Gelfand-Gelfand resolution of a finite dimensional, irreducible g-module, Trans. Amer. Math. Soc., to appear.
N. N. Šapovalov, On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra, Funkcional. Analiz. i Priložen, 6, no. 4 (1972), 65–70 = Functional Anal. Appl. 6 (1972), 307–312.
V. S. Varadarajan, Infinitesimal theory of representations of semisimple Lie groups, lectures given at NATO Advanced Study Institute, Liège, 1977.
D. A. Vogan, Irreducible characters of semisimple Lie groups II Duke Math. J. 46(1979), 805–859.
N. R. Wallach, On the Enright-Varadarajan modules: A construction of the discrete series, Ann. Sci. École Norm Sup. (4) 9 (1976), 81–102.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer-Verlag
About this chapter
Cite this chapter
Humphreys, J.E. (1980). Highest weight modules for semisimple Lie algebras. In: Dlab, V., Gabriel, P. (eds) Representation Theory I. Lecture Notes in Mathematics, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089779
Download citation
DOI: https://doi.org/10.1007/BFb0089779
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10263-2
Online ISBN: 978-3-540-38385-7
eBook Packages: Springer Book Archive
