Skip to main content
SpringerLink
Log in

Resolutions of irreducible highest weight modules over infinite dimensional graded lie algebras

  • Conference paper
  • First Online:
Lie Algebras and Related Topics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 933))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. I.N. Bernstein, I.M. Gelfand and S.I. Gelfand: Category of g-nodules, English translation from Funktsional’nyi Analiz i Ego Prilozheniya, (2) 10 (1976), 1–8.

    MathSciNet  Google Scholar 

  2. -: Differential operators on the base affine space and a study of g-modules, Lie groups and their representations Proc. Summer School on Group Representations (I.M. Gelfand, ed.), Bolyai János Math. Soc., Wiley, New York, 1975, 39–69.

    Google Scholar 

  3. -: Structure of representations generated by vectors of highest weight, English translation from Funktsional’nyi Analiz i Ego Prilozheniya (1) 5 (1971), 1–9.

    Google Scholar 

  4. J. Dixmier: Enveloping Algebras, North-Holland Math. Library 14, North-Holland, New York, 1977.

    MATH  Google Scholar 

  5. T. Enright: On the fundamental series of a real semi-simple Lie algebra: their irreducibility, resolutions and multiplicity formulae. Annals of Math., 110 (1979), 1–82.

    Article  MathSciNet  MATH  Google Scholar 

  6. T. Enright and N. R. Wallach: The fundamental series of representations of a real semi-simple Lie algebra, Acta Math. 140 (1978), 1–32.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Garland and J. Lepowsky: Lie algebra homology and the Macdonald-Kac formulas, Inv. Math. 34 (1976), 37–76.

    Article  MathSciNet  MATH  Google Scholar 

  8. L.V. Goncharova: The cohomologies of Lie algebras of formal vector fields on the line, English translation from Funktsional’nyi Analiz i Ego Prilozheniya, (2) 7 (1973), 6–14.

    Google Scholar 

  9. -: Cohomologies of Lie algebras of formal vector fields on the straight line, English translation from Funktsional’nyi Analiz i Ego Prilozheniya (3) 7 (1973), 33–44.

    Google Scholar 

  10. J.C. Jantzen: Moduln mit einem höchsten Gewicht, Lecture Notes in Mathematics 750, Springer-Verlag, New York, 1979.

    MATH  Google Scholar 

  11. V.G. Kac: Contravariant form for Lie algebras and superalgebras, Lecture Notes in Physics 94, Springer-Verlag, New York (1979), 441–445.

    MATH  Google Scholar 

  12. V.G. Kac: Infinite-dimensional Lie algebras and Dedekind’s η-function, Funct. Anal. Appl. 8 (1974), 68–70.

    Article  MathSciNet  MATH  Google Scholar 

  13. V.G. Kac: Simple irreducible graded Lie algebras of finite growth. Math. USSR Izv. 2 (1968), 1271–1311.

    Article  MATH  Google Scholar 

  14. V.G. Kac and D.A. Kazhdan: Structure of representations with highest weight of infinite dimensional Lie algebras, Advances in Math. 1 (34) (1979), 97–108.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Lepowsky: A generalization of the Bernstein-Gelfand-Gelfand resolution, J. Algebra (2) 49 (1977), 496–511.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Lepowsky: Lectures on Kac-Moody Lie algebras, Université de Paris VI (1978) (mineographed notes).

    Google Scholar 

  17. B. Mitchell: Theory of Categories, Pure and Applied Mathematics XVII, Academic press, New York, 1965.

    Google Scholar 

  18. R.V. Moody: A new class of Lie algebras, Journal of Algebra 10 (1968), 211–230.

    Article  MathSciNet  MATH  Google Scholar 

  19. -: Macdonald identities and Euclidean Lie algebras, Proc. Amer. Math. Soc. 48 (1975), 43–52.

    Article  MathSciNet  MATH  Google Scholar 

  20. A Rocha-Caridi: Splitting criteria for g-modules induced from a parabolic and the Bernstein-Gelfand-Gelfand resolution of a finite dimensional irreducible g-module, Ph.D. Thesis, Rutgers University, 1978.

    Google Scholar 

  21. -: Splitting criteria for g-modules induced from a parabolic and the Bernstein-Gelfand-Gelfand resolution of a finite dimensional irreducible g-module, Transactions of the A.M.S. (2) 262 (1980), 335–336.

    MathSciNet  MATH  Google Scholar 

  22. A. Rocha-Caridi and N.R. Wallach: Eighest weight modules over graded Lie algebras: Resolutions, filtrations and character formulas, to appear.

    Google Scholar 

  23. A. Rocha-Caridi: Projective modules over graded Lie algebras I, to appear.

    Google Scholar 

  24. N.R. Wallach: On the Enright-Varadarajan modules, a construction of the discrete series, Ann. Sci. Ecole Norm. Sup., (4) 9 (1976), 81–102.

    MathSciNet  MATH  Google Scholar 

  25. N.R. Wallach: Unpublished manuscript notes on the Borel-Weil theorem.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rutgers University, 08903, New Brunswick, NJ

    Alvany Rocha-Caridi

Authors
  1. Alvany Rocha-Caridi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

David Winter

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Rocha-Caridi, A. (1982). Resolutions of irreducible highest weight modules over infinite dimensional graded lie algebras. In: Winter, D. (eds) Lie Algebras and Related Topics. Lecture Notes in Mathematics, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093361

Download citation

  • DOI: https://doi.org/10.1007/BFb0093361

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11563-2

  • Online ISBN: 978-3-540-39262-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation