Skip to main content

An application of the serre conjecture to semisimple algebraic groups

Group Theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 848)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, Mass., 1969.

    MATH  Google Scholar 

  2. A. Borel, Linear Algebraic Groups, W. A. Benjamin, New York, 1969.

    MATH  Google Scholar 

  3. N. Bourbaki, Algèbre commutative, Chapitres 1 et 2, Hermann, Paris, 1961.

    MATH  Google Scholar 

  4. N. Bourbaki, Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris, 1968.

    MATH  Google Scholar 

  5. A. Cohen, "Finite complex reflection groups," Ann. Scient. Ec. Norm. Sup. (4) 9 (1976), 379–436.

    MathSciNet  MATH  Google Scholar 

  6. D. Ferrand, Séminaire Bourbaki, exposé 484, Lecture Notes no. 567, Springer-Verlag, Berlin-Heidelberg-New York, 1977.

    Google Scholar 

  7. B. Kostant, "Lie group representations on polynomial ring," Amer. J. Math. 85 (1963), 327–404.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. B. Kostant and S. Rallis, "Orbits and representations associated with symmetric spaces," Amer. J. Math. 93 (1971), 753–809.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. D. Luna and R. Richardson, "A generalization of the Chevalley restriction theorem," Duke Math. J. 46 (1979), 487–497.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. H. Matsumura, Commutative Algebra, W. A. Benjamin, New York, 1970.

    MATH  Google Scholar 

  11. H. Pittie, "Homogeneous vector bundles on homogeneous spaces," Topology 11 (1972), 199–203.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. D. Quillen, "Projective modules over polynomial rings," Inventiones Math. 36 (1976), 167–171.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. R. Richardson, "The conjugating representation of a semisimple group," Inventiones Math. 54 (1979), 229–246.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. R. Richardson, "Invariants, orbits and representations associated to involutions of reductive groups" (to appear).

    Google Scholar 

  15. G. Schwarz, "Representations of simple Lie groups with a free module of covariants," Inventiones Math. 50 (1978), 1–12.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. G. Shephard and J. Todd, "Finite unitary reflection groups," Canad. J. Math. 6 (1954), 274–304.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. T. A. Springer, Invariant Theory, Lecture Notes no. 585, Springer-Verlag, Berlin-Heidelberg-New York, 1977.

    CrossRef  Google Scholar 

  18. R. Steinberg, "Regular elements of semisimple algebraic groups," Publ. Math. I.H.E.S. 25 (1965), 49–80.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. R. Steinberg, "On a theorem of Pittie," Topology 14 (1975), 173–177.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. A. Suslin, "Projective modules over a polynomial ring," (in Russian), Dokl. Akad. Nauk. S.S.R. 26 (Feb. 1976).

    Google Scholar 

  21. R. Richardson, "Principal orbit types for algebraic transformation spaces in characteristic zero," Inventiones Math. 16 (1972), 6–14.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Richardson, R.W. (1981). An application of the serre conjecture to semisimple algebraic groups. In: Amayo, R.K. (eds) Algebra Carbondale 1980. Lecture Notes in Mathematics, vol 848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090561

Download citation

  • DOI: https://doi.org/10.1007/BFb0090561

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10573-2

  • Online ISBN: 978-3-540-38549-3

  • eBook Packages: Springer Book Archive