Skip to main content
SpringerLink
Log in

Stable Distributions Supported on the Nilpotent Cone for the Group G 2

  • Chapter
The Unity of Mathematics

Part of the book series: Progress in Mathematics ((PM,volume 244))

Abstract

Assuming that p is sufficiently large, we describe the stable distributions supported on the set of nilpotent elements for p-adic G2.

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 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. D. Adler, Refined anisotropic K-types and supercuspidal representations, Pacific J. Math., 185 (1998), 1–32.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Adler and S. DeBacker, Some applications of Bruhat-Tits theory to harmonic analysis on the Lie algebra of a reductive p-adic group, Michigan Math. J., 50-2 (2002), 263–286.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Adler and S. DeBacker, A generalization of a result of Kazhdan and Lusztig, Proc. Amer. Math. Soc., 132-6 (2004), 1861–1868 (electronic).

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Adler and S. DeBacker, Murnaghan-Kirillov theory for supercuspidal representations of tame general linear groups, J. Reine Angew. Math., 575 (2004), 1–35.

    MATH  MathSciNet  Google Scholar 

  5. J. Adler and A. Roche, An intertwining result for p-adic groups, Canad. J. Math., 52-3 (2000), 449–467.

    MATH  MathSciNet  Google Scholar 

  6. D. Barbasch and A. Moy, Local character expansions, Ann. Sci. École Norm. Sup. (4), 30-5 (1997), 553–567.

    MATH  MathSciNet  Google Scholar 

  7. A. Borel, Linear Algebraic Groups, 2nd enlarged ed., Graduate Texts in Mathematics 126, Springer-Verlag, New York, 1991.

    MATH  Google Scholar 

  8. F. Bruhat and J. Tits, Groupes réductifs sur un corps local II: Schémas en groupes. Existence d’une donnée radicielle valuée, Inst. Hautes Études Sci. Publ. Math., 60 (1984), 197–376.

    MathSciNet  Google Scholar 

  9. F. Bruhat and J. Tits, Groupes algébriques sur un corps local, Chapitre III: Compléments et applications la cohomologie galoisienne, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 34-3 (1987), 671–698.

    MATH  MathSciNet  Google Scholar 

  10. R. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, reprint of the 1985 original, Wiley Classics Library, Wiley, Chichester, UK, 1993.

    Google Scholar 

  11. S. DeBacker, Homogeneity results for invariant distributions of a reductive p-adic group, Ann. Sci. École Norm. Sup. (4), 35-3 (2002), 391–422.

    MATH  MathSciNet  Google Scholar 

  12. S. DeBacker, Parametrizing nilpotent orbits via Bruhat-Tits theory, Ann. Math. (2), 156-1 (2002), 295–332.

    Article  MATH  MathSciNet  Google Scholar 

  13. S. DeBacker, Parametrizing conjugacy classes of maximal unramified tori, Michigan Math. J, to appear.

    Google Scholar 

  14. Harish-Chandra, Harmonic Analysis on Reductive p-Adic Groups, notes by G. van Dijk, Lecture Notes in Mathematics 162, Springer-Verlag, Berlin, New York, 1970.

    MATH  Google Scholar 

  15. Harish-Chandra, Admissible Invariant Distributions on Reductive p-Adic Groups, preface and notes by S. DeBacker and P. J. Sally, Jr., University Lecture Series 16, American Mathematical Society, Providence, RI, 1999.

    MATH  Google Scholar 

  16. R. Howe, Two conjectures about reductive p-adic groups, in C. C. Moore, ed., Harmonic Analysis on Homogeneous Spaces, Proceedings of Symposia in Pure Mathematics 26, American Mathematical Society, Providence, RI, 1973, 377–380.

    Google Scholar 

  17. R. Howlett and G. Lehrer, On Harish-Chandra induction and restriction for modules of Levi subgroups, J. Algebra, 165-1 (1994), 172–183.

    Article  MATH  MathSciNet  Google Scholar 

  18. N. Kawanaka, Shintani lifting and Gelfand-Graev representations, in P. Fong, ed., The Arcata Conference on Representations of Finite Groups, Proceedings of Symposia in Pure Mathematics 47, Part 1, American Mathematical Society, Providence, RI, 1987, 147–163.

    Google Scholar 

  19. D. Kazhdan, Proof of Springer’s hypothesis, Israel J. Math., 28 (1977), 272–286.

    MATH  MathSciNet  Google Scholar 

  20. D. Kazhdan and G. Lusztig, Fixed point varieties on affine flag manifolds, Israel J. Math., 62-2 (1988), 129–168.

    MATH  MathSciNet  Google Scholar 

  21. G. Lusztig, Fourier transforms on a semisimple Lie algebra over F q, in W. H. Hesselink, W. L. J. Van Der Kallen, A. M. Cohen, T.A. Springer, J.R. Strooker, and A. M. Cohen, eds., Algebraic Groups: Utrecht 1986, Lecture Notes in Mathematics 1271, Springer-Verlag, Berlin, 1987, 177–188.

    Chapter  Google Scholar 

  22. G. Lusztig, Green functions and character sheaves, Ann. Math., 131 (1990), 355–408.

    Article  MathSciNet  Google Scholar 

  23. G. Lusztig, A unipotent support for irreducible representations, Adv. Math., 94-2 (1992), 139–179.

    Article  MATH  MathSciNet  Google Scholar 

  24. A. Moy and G. Prasad, Unrefined minimal K-types for p-adic groups, Invent. Math., 116 (1994), 393–408.

    Article  MATH  MathSciNet  Google Scholar 

  25. N. Spaltenstein, On the Kazhdan-Lusztig map for exceptional Lie algebras, Adv. Math., 83-1 (1990), 48–74.

    Article  MATH  MathSciNet  Google Scholar 

  26. T. Springer, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. Math., 36 (1976), 173–207.

    Article  MATH  MathSciNet  Google Scholar 

  27. J.-L. Waldspurger, Transformation de Fourier et endoscopie, J. Lie Theory, 10-1 (2000), 195–206.

    MATH  MathSciNet  Google Scholar 

  28. J.-L. Waldspurger, Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés, Astérisque 269, Société Mathématique de France, Paris, 2001.

    MATH  Google Scholar 

  29. J.-L. Waldspurger, Quelques résultats de finitude conçernant les distributions invariantes sur les algèbres de Lie p-adiques, preprint, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI, 48109-1043, USA

    Stephen DeBacker

  2. Institute of Mathematics, Hebrew University, Givat-Ram, Jerusalem, 91904, Israel

    David Kazhdan

Authors
  1. Stephen DeBacker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Kazhdan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Pavel Etingof  & I. M. Singer  & 

  2. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Vladimir Retakh

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Birkhäuser Boston

About this chapter

Cite this chapter

DeBacker, S., Kazhdan, D. (2006). Stable Distributions Supported on the Nilpotent Cone for the Group G 2 . In: Etingof, P., Retakh, V., Singer, I.M. (eds) The Unity of Mathematics. Progress in Mathematics, vol 244. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4467-9_6

Download citation

Publish with us

Policies and ethics

Search

Navigation