Descent for Transfer Factors

  • R. Langlands
  • D. Shelstad
Part of the Modern Birkhäuser Classics book series (MBC)


In [I] we introduced the notion of transfer from a group over a local field to an associated endoscopic group, but did not prove its existence, nor do we do so in the present paper. Nonetheless we carry out what is probably an unavoidable step in any proof of existence: reduction to a local statement at the identity in the centralizer of a semisimple element, a favorite procedure of Harish Chandra that he referred to as descent.


Conjugacy Class Galois Group Transfer Factor Dynkin Diagram Borel Subgroup 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [I]
    R. Langlands and D. Shelstad, On the definition of transfer factors, Math. Ann., 278, 219–271 (1987).MATHCrossRefMathSciNetGoogle Scholar
  2. [B]
    N. Bourbaki, Groupes et Algèbres de Lie, Chs. 4, 5, 6, Hermann (1968).Google Scholar
  3. [C-D]
    L. Clozel and P. Delorme, Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs, Inv. Math. 77, 427–453 (1984).MATHCrossRefMathSciNetGoogle Scholar
  4. [HC1]
    Harish-Chandra, Invariant eigendistributions on a semisimple Lie group, Trans. Amer. Math. Soc, 119, 457–508 (1965).MATHCrossRefMathSciNetGoogle Scholar
  5. [HC2]
    (notes by G. van Dijk) Harmonic Analysis on Reductive p-adic Groups, Springer Lecture Notes, Vol. 162 (1970)Google Scholar
  6. [HC3]
    Harmonic analysis on real reductive groups I, J. Funct. Anal., 19, 104–204 (1975).MATHCrossRefMathSciNetGoogle Scholar
  7. [K1]
    R. Kottwitz, Rational conjugacy classes in reductive groups, Duke Math. J., 49, 785–806 (1982).MATHCrossRefMathSciNetGoogle Scholar
  8. [K2]
    Stable trace formula: elliptic singular terms, Math. Ann., 275, 365–399 (1986).MATHCrossRefMathSciNetGoogle Scholar
  9. [K3]
    Tamagawa. numbers, Ann. of Math., 127, 629–646 (1988).CrossRefMathSciNetGoogle Scholar
  10. [K4]
    Sign changes in harmonic analysis on reductive groups, Trans. Amer. Math. Soc, 278, 289–297 (1983).MATHCrossRefMathSciNetGoogle Scholar
  11. [K-S]
    _____ and D. Shelstad, Twisted endoscopy, in prepara-tion.Google Scholar
  12. [L1]
    R. Langlands, Les Débuts d’une Formule des Traces Stable, Publ. Math. Univ. Paris VII, Vol. 13 (1983).Google Scholar
  13. [L2]
    Stable conjugacy: definitions and lemmas, Can. J. Math., 31, 700–725 (1979).MATHMathSciNetGoogle Scholar
  14. [L3]
    Representations of abelian algebraic groups, preprint (1968).Google Scholar
  15. [L-S]
    _____ and D. Shelstad, Orbital integrals on forms of SL(3), II, Can. J. Math. (in press).Google Scholar
  16. [M]
    J.S. Milne, Arithmetic Duality Theorems, Academic Press (1986).Google Scholar
  17. [Se]
    J.-P. Serre, Corps Locaux, Hermann (1962).Google Scholar
  18. [S1]
    D. Shelstad, Characters and inner forms of a quasi-split group over R, Comp. Math., 39, 11–45 (1979).MATHMathSciNetGoogle Scholar
  19. [S2]
    Orbital integrals and a family of groups attached to a real reductive group, Ann. Sci. Ec. Norm. Sup., 12, 1–31 (1979).Google Scholar
  20. [S3]
    Embeddings of L-groups, Can. J. Math., 33, 513–558 (1981).MATHMathSciNetGoogle Scholar
  21. [S4]
    L-indistinguishability for real groups, Math. Ann., 259, 385–430 (1982).MATHCrossRefMathSciNetGoogle Scholar
  22. [S5]
    Orbital integrals, endoscopic groups and L-indistinguishability for real groups, Publ. Math. Univ. Paris VII, Vol. 15 (1984).Google Scholar
  23. [W]
    G. Warner, Harmonic Analysis on Semisimple Lie Groups, Vol. II, Springer Verlag (1972).Google Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • R. Langlands
    • 1
    • 2
    • 3
  • D. Shelstad
    • 1
    • 2
    • 3
  1. 1.School of MathematicsThe Institute for Advanced StudyPrinceton
  2. 2.Mathematics DepartmentThe University of UtahSalt Lake City
  3. 3.Mathematics DepartmentRutgers UniversityNewark

Personalised recommendations