Skip to main content

Lifting of Characters

  • Chapter

Part of the book series: Progress in Mathematics ((PM,volume 101))

Abstract

In Lifting of Characters and Harish-Chandra’s Method of Descent [1] we discussed lifting of characters from endoscopic groups in terms which we need for Arthur's conjectures [4]. This paper is an expository version of [1], written with some important special cases in mind and illustrated by numerous examples. We refer the reader to the introduction to [1] for motivation; here we limit ourselves to a summary of some essential points and a discussion of how this paper differs from [1].

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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. J. Adams and D. Vogan, Lifting of Characters and Harish-Chandra’s Method of Descent, submitted to Journal of AMS (preprint).

    Google Scholar 

  2. J. Adams and D. Vogan, L-Groups, Projective Representations, and the Langlands Classification, to appear in Amer. Journal Math.

    Google Scholar 

  3. J. Adams and D. Vogan, Lifting of Characters and Harish-Chandra’s Method of Descent, to appear in Amer. Journal Math.

    Google Scholar 

  4. J. Arthur, On Some Problems Suggested By the Trace Formula, in Proc. of the Special Year in Harmonic Analysis, University of Maryland, R. Herb, Ft. Lipsman and J. Rosenberg, eds., SLN, vol. 1024, Springer-Verlag, New York, 1983.

    Google Scholar 

  5. A. Borel, Automorphic L-Functions, Proc. Symp. Pure Math., vol. 33, American Math. Soc, Providence, Rhode Island, 1979.

    Google Scholar 

  6. Harish-Chandra, Invariant Eigendistributions on a Semi-simple Lie Group, Trans. Amer. Math. Soc. 119 (1965), 457–508.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Helgason, in Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.

    Google Scholar 

  8. R. Langlands, On the Classification of Irreducible Representations of Real Algebraic Groups, in Representation Theory and Harmonic Analysis on Semisimple Lie Groups, P. Sally, D. Vogan, eds., Mathematical Surveys and Monographs, vol. 31, AMS, Providence, 1989.

    Google Scholar 

  9. D. Shelstad, Orbital Integrals and a Family of Groups attached to a Real Reductive Group, Ann. École Nat. Sup. Méc. Nantes 12 (1979), 1–31.

    MathSciNet  Google Scholar 

  10. D. Shelstad, L-Indistinguishability for Real Groups, Math. Ann. 259 (1982), 385–430

    Article  MathSciNet  MATH  Google Scholar 

  11. R. Steinberg, Regular Elements of Semisimple Algebraic Groups, Publ. I.H.E.S. (1965).

    Google Scholar 

  12. D. Vogan, Representations of Real Reductive Lie Groups, Birkhauser, Boston, 1981.

    MATH  Google Scholar 

  13. D. Vogan, Irreducible Characters of Semisimple Lie Groups IV. Character- Multiplicity Duality, Duke Math. J. 49, No. 4 (1982), 943–1073.

    Article  MathSciNet  MATH  Google Scholar 

  14. G. Zuckerman, Tensor Products of Finite and Infinite Dimensional Representations of Semisimple Lie Groups, Ann. of Math. (2) (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Adams, J. (1991). Lifting of Characters. In: Barker, W.H., Sally, P.J. (eds) Harmonic Analysis on Reductive Groups. Progress in Mathematics, vol 101. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0455-8_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0455-8_1

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6768-3

  • Online ISBN: 978-1-4612-0455-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics