Skip to main content
SpringerLink
Log in

The fourier transform of orbital integrals on SL2 over a p-adic field

  • Conference paper
  • First Online:
Lie Group Representations II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1041))

Both authors supported by the National Science Foundation

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
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.

Bibliography

  1. W. Casselman, The Steinberg character as a true character, PSPM XXVI, AMS, Providence, 1973, pp. 413–418.

    MATH  Google Scholar 

  2. L. E. Dickson, Linear Groups, Dover, New York, 1958.

    Google Scholar 

  3. S. Franklin, The Reducible Principal Series of SL(2) over a p-adic Field, Thesis, University of Chicago, 1971.

    Google Scholar 

  4. I. M. Gel'fand and M. I. Graev, Representations of a group of the second order with elements from a locally compact field, Uspehi Mat. Nauk = Russian Math. Surveys 18(1963), 29–100.

    Article  MathSciNet  MATH  Google Scholar 

  5. P. J. Sally, Jr., Invariant subspaces and Fourier-Bessel transforms on the p-adic plane, Math. Ann. 174(1967), 247–264.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. J. Sally, Jr., Unitary and uniformly bounded representations of the two by two unimodular group over local fields, Amer. J. Math. 90(1968), 406–443.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Scott, The Fourier Transform of Orbital Integrals on GL(2) over a p-adic Field, Thesis, University of Chicago, 1983.

    Google Scholar 

  8. J. A. Shalika, Representations of the Two by Two Unimodular Group over Local Fields, Thesis, The Johns Hopkins University, 1966.

    Google Scholar 

  9. J. A. Shalika, A theorem on semisimple p-adic groups, Annals of Math. 95(1972), 226–242.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. A. Shalika, On the space of cusp forms of a p-adic Chevalley group, Annals of Math. 92(1970), 262–278.

    Article  MathSciNet  MATH  Google Scholar 

  11. P. J. Sally, Jr. and J. A. Shalika, Characters of the discrete series of representations of SL(2) over a local field, Proc. Nat. Acad. Sci. U. S. A. 61(1968), 1231–1237.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. J. Sally, Jr. and J. A. Shalika, The Plancherel formula for SL(2) over a local field, Proc. Nat. Acad. Sci. U. S. A. 63(1969), 661–667.

    Article  MathSciNet  MATH  Google Scholar 

  13. P. J. Sally, Jr. and M. H. Taibleson, Special functions on locally compact fields, Acta Math. 116(1966), 279–309.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Tanaka, On irreducible unitary representations of some special linear groups of the second order, I, Osaka J. Math. 3(1966), 217–227.

    MathSciNet  MATH  Google Scholar 

Additional References for Orbital Integrals on p-adic Groups

  1. L. Clozel, Sur une conjecture de Howe–I, preprint.

    Google Scholar 

  2. D. Flath, A comparison of the automorphic representations of GL(3) and its twisted forms, Pacific J.Math. 97(1981), 373–402.

    Article  MathSciNet  MATH  Google Scholar 

  3. Y. Flicker, The Trace Formula and Base Change for GL(3), SLN 927, Springer, Berlin, 1982.

    Google Scholar 

  4. R. Howe, Two conjectures about reductive p-adic groups, PSPM XXVI, AMS, 1973, pp. 377–380.

    Google Scholar 

  5. R. Howe, The Fourier transform and germs of characters (case of GLn over a p-adic field), Math. Ann. 208(1974), 305–322.

    Article  MathSciNet  MATH  Google Scholar 

  6. Harish-Chandra, Harmonic Analysis on Reductive p-adic Groups, SLN 162, Springer, Berlin, 1970.

    Book  MATH  Google Scholar 

  7. Harish-Chandra, Harmonic analysis on reductive p-adic groups, PSPM XXVI, AMS, Providence, 1973, pp. 167–192.

    MATH  Google Scholar 

  8. Harish-Chandra, Admissible distributions on reductive p-adic groups, Lie Theories and Their Applications, Queen's Papers in Pure and Applied Mathematics, Queen's University, Kingston, Ontario, 1978, pp. 281–347.

    Google Scholar 

  9. R. Kottwitz, Orbital integrals and base change, PSPM XXXIII, AMS, 1979, Part 2, pp. 185–192.

    Google Scholar 

  10. R. Kottwitz, Orbital integrals on GL3, Amer. J. Math. 102(1980), 327–384.

    Article  MathSciNet  MATH  Google Scholar 

  11. R. Kottwitz, Unstable orbital integrals on SL(3), Duke Math. J. 48(1981), 649–664.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. P. Langlands, Base Change for GL(2), Princeton, 1980.

    Google Scholar 

  13. R. P. Langlands, Les debuts d'une formule des traces stables, preprint.

    Google Scholar 

  14. R. P. Langlands, Orbital integrals on forms of SL(3), Amer. J. Math. 105(1983), 465–506.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. P. Labesse and R. P. Langlands, L-indistinguishability for SL(2), Can. J. Math. 31(1979), 726–785.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. Ranga Rao, Orbital integrals in reductive groups, Annals of Math. 96(1972), 505–510.

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Repka,Shalika's germs for p-adic GL(n): the leading term, preprint.

    Google Scholar 

  18. J. Repka,Shalika's germs for p-adic GL(n), II: the subregular term, preprint.

    Google Scholar 

  19. J. Repka, Germs associated to regular unipotent classes in p-adic SL(n), preprint.

    Google Scholar 

  20. J. Rogawski, An application of the building to orbital integrals, Compositio Math. 42(1981), 417–423.

    MathSciNet  MATH  Google Scholar 

  21. J. Rogawski, Representations of GL(n) and division algebras over a p-adic field, Duke Math. J. 50(1983), 161–196.

    Article  MathSciNet  MATH  Google Scholar 

  22. J. Rogawski, Some remarks on Shalika germs, preprint.

    Google Scholar 

  23. A. Silberger, Introduction to Harmonic Analysis on Reductive p-adic Groups, Princeton, 1979.

    Google Scholar 

  24. M-F. Vigneras, Caractérisation des intégrales orbitales sur un groupe réductif p-adique, J. Fac. Sci., University of Tokyo 28(1981), 945–961.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Chicago, 60637, Chicago, IL

    Paul J. Sally Jr. & Joseph A. Shalika

  2. Department of Mathematics, Johns Hopkins University, 21218, Baltimore, MD

    Paul J. Sally Jr. & Joseph A. Shalika

Authors
  1. Paul J. Sally Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joseph A. Shalika
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rebecca Herb Stephen Kudla Ronald Lipsman Jonathan Rosenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Sally, P.J., Shalika, J.A. (1983). The fourier transform of orbital integrals on SL2 over a p-adic field. In: Herb, R., Kudla, S., Lipsman, R., Rosenberg, J. (eds) Lie Group Representations II. Lecture Notes in Mathematics, vol 1041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073152

Download citation

  • DOI: https://doi.org/10.1007/BFb0073152

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12715-4

  • Online ISBN: 978-3-540-38699-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation