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International Mathematics Research Papers (2008) Vol. 2008 : article ID rpn003, 95 pages, doi:10.1093/imrp/rpn003 published on May 30, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Good Product Expansions for Tame Elements of p-Adic Groups

Jeffrey D. Adler1 and Loren Spice2

1 Department of Mathematics and Statistics, American University, 4400 Massachusetts Ave NW, Washington, DC 20016-8050, USA
2 The University of Michigan, Ann Arbor, MI 48109-1043, USA

Correspondence: Correspondence to be sent to: jadler{at}american.edu

We show that, under fairly general conditions, many elements of a p-adic group can be well approximated by a product whose factors have properties that are helpful in performing explicit character computations.



References

  1. Adler J. D. Refined anisotropic K-types and supercuspidal representations. Pacific Journal of Mathematics (1998) 185:1–32.[ISI]
  2. Adler J. D., Corwin L., Sally P. J. Jr. Discrete series characters of division algebras and GLn over a p-adic field. In: Contributions to Automorphic Forms, Geometry, and Number Theory (2004) Baltimore, MD: Johns Hopkins University Press. 57–64.
  3. Adler J. D., DeBacker S. Some applications of Bruhat–Tits theory to harmonic analysis on the Lie algebra of a reductive p-adic group. Michigan Mathematical Journal (2002) 50:263–86.[CrossRef][ISI]
  4. Adler J. D., DeBacker S. Murnaghan–Kirillov theory for supercuspidal representations of tame general linear groups. Journal für die Reine und Angewandte Mathematik (2004) 575:1–35.[ISI]
  5. Adler J. D., Spice L. Supercuspidal characters of reductive p-adic groups. (2007) preprint arXiv:0707.3313.
  6. Boller J. Characters of some supercuspidal representations of p-adic Sp4(F). (1999) PhD Thesis, The University of Chicago.
  7. Borel A. Linear Algebraic Groups (1991) New York: Springer. Graduate Texts in Mathematics 126.
  8. Borel A., Springer T. A. Rationality properties of linear algebraic groups 2. Tôhoku Mathematical Journal (1968) 20(no. 2):443–97.[CrossRef]
  9. Borel A., Tits J. Groupes réductifs. Publications Mathématiques de l'Institut des Hautes Études Scientifiques (1965) 27:55–150.[CrossRef]
  10. Borel A., Tits J. Homomorphismes ‘abstraits’ de groupes algébriques simples. Annals of Mathematics (1973) 97(no. 2):499–571.[CrossRef][ISI]
  11. Bourbaki N. Lie Groups and Lie Algebras. (2002) Chap. 4–6, Elements of Mathematics. Berlin: Springer.
  12. Bruhat F., Tits J. Groupes réductifs sur un corps local. Publications Mathématiques de l'Institut des Hautes Études Scientifiques (1972) 41:5–251.[CrossRef]
  13. Bruhat F., Tits J. Groupes réductifs sur un corps local 2: Schémas en groupes. Existence d'une donnée radicielle valuée. Publications Mathématiques de l'Institut des Hautes Études Scientifiques (1984) 60:197–376.
  14. Corwin L., Moy A., Sally P. J. Jr. Supercuspidal character formulas for Formula . In: Representation theory and harmonic analysis (1995) Providence, RI: American Mathematical Society. 1–11. Contemporary Mathematics 191.
  15. DeBacker S. On supercuspidal characters of GL{ell}, {ell} a prime. (1997) PhD Thesis, The University of Chicago.
  16. DeBacker S. Some applications of Bruhat–Tits theory to harmonic analysis on a reductive p-adic group. Michigan Mathematical Journal (2002) 50:241–61.[CrossRef][ISI]
  17. DeBacker S. Parametrizing nilpotent orbits via Bruhat–Tits theory. Annals of Mathematics (2002) 156(no. 2):295–332.[CrossRef][ISI]
  18. Gérardin P. Sur les représentations du groupe linéaire général sur un corps p-adique. In: Séminaire Delange-Pisot-Poitou (1973) Paris: Secrétariat Mathématique. 1–24. Théorie des nombres 14.
  19. Grothendieck A. Éléments de géométrie algébrique 4: Étude locale des schémas et des morphismes de schémas 4. Publications Mathématiques de l'Institut des Hautes Études Scientifiques (1967) 32.
  20. Hales T. C. A simple definition of transfer factors for unramified groups. In: Representation theory and harmonic analysis (1993) Providence, RI: American Mathematical Society. 109–34. Contemporary Mathematics 145.
  21. Kazhdan D. On lifting. In: Lie Group Representations 2 (1984) Berlin: Springer. 209–49. Lecture Notes in Mathematics 1041.
  22. Kim J.-L., Murnaghan F. Character expansions and unrefined minimal K-types. American Journal of Mathematics (2003) 125:1199–234.[CrossRef][ISI]
  23. Kottwitz R. E. Isocrystals with additional structure 2. Compositio Mathematica (1997) 109:255–339.[CrossRef][ISI]
  24. Kutzko P. C. On the supercuspidal representations of Formula . American Journal of Mathematics (1978) 100:43–60.[CrossRef][ISI]
  25. Landvogt E. A compactification of the Bruhat–Tits building (1996) Berlin: Springer. Lecture Notes in Mathematics 1619.
  26. Lang S. On quasi algebraic closure. Annals of Mathematics (1952) 55(no. 2):373–90.[CrossRef][ISI]
  27. Moy A. Displacement functions on the Bruhat–Tits building. In: The Mathematical Legacy of Harish-Chandra (2000) Providence, RI: American Mathematical Society. 483–99. Proceedings of Symposia in Pure Mathematics 68.
  28. Moy A., Prasad G. Unrefined minimal K-types for p-adic groups. Inventiones Mathematicae (1994) 116:393–408.[CrossRef][ISI]
  29. Moy A., Prasad G. Jacquet functors and unrefined minimal K-types. Commentarii Mathematici Helvetici (1996) 71:98–121.[CrossRef][ISI]
  30. Murnaghan F. Characters of supercuspidal representations of SL(n). Pacific Journal of Mathematics (1995) 170:217–35.[ISI]
  31. Murnaghan F. Local character expansions and Shalika germs for GL(n). Mathematische Annalen (1996) 304:423–55.[CrossRef][ISI]
  32. Prasad G., Yu J.-K. On finite group actions on reductive groups and buildings. Inventtiones Mathematicae (2002) 147:545–60.[CrossRef]
  33. Rapoport M. The reduction of the Shimura variety associated to a torus. Forthcoming.
  34. Roche A. Types and Hecke algebras for principal series representations of split reductive p-adic groups. Annales Scientifiques de l'École Normale Supérieure (1998) 31(no. 4):361–413.[CrossRef]
  35. Rousseau G. Immeubles des groupes réductifs sur les corps locaux. (1977) PhD Thesis, University Paris XI.
  36. Sally P. J. Jr, Shalika J. A. Characters of the discrete series of representations of SL(2) over a local field. Proceedings of the National Academy of Sciences of the United States of America (1968) 61:1231–7.[Free Full Text]
  37. Serre J.-P. Local Fields (1979) New York: Springer. Graduate Texts in Mathematics 67.
  38. Serre J.-P. Lie Algebras and Lie Groups (1992) Berlin: Springer. Lecture Notes in Mathematics 1500.
  39. Serre J.-P. Galois Cohomology (2002) Berlin: Springer. Springer Monographs in Mathematics.
  40. Shimizu H. Some examples of new forms. Journal of the Faculty of Science: University of Tokyo Section IA: Mathematics (1977) 24:97–113.
  41. Silberger A. J. PGL2 over the p-adics: Its representations, Spherical Functions, and Fourier Analysis (1970) Berlin: Springer. Lecture Notes in Mathematics 166.
  42. Spice L. Supercuspidal characters of Formula over a p-adic field, {ell} a prime. American Journal of Mathematics (2005) 127:51–100.[CrossRef][ISI]
  43. Spice L. Topological Jordan decompositions. Journal of Algebra (2008) 319:3141–63.[ISI]
  44. Springer T. A. Linear Algebraic Groups (1998) Boston, MA: Birkhäuser Boston. Progress in Mathematics 9.
  45. Springer T. A., Steinberg R. Conjugacy classes. In: Seminar on Algebraic Groups and Related Finite Groups (1970) Berlin: Springer. 167–266. Lecture Notes in Mathematics 131.
  46. Tits J. Reductive groups over local fields. In: Automorphic Forms, Representations, and L-Functions: Part 1 (1979) Providence, RI: American Mathematical Society. 29–69. Proceedings of Symposia in Pure Mathematics 33.
  47. Weil A. Basic Number Theory (1973) 2nd ed. New York: Springer.
  48. Yu J.-K. Construction of tame supercuspidal representations. Journal of the American Mathematical Society (2001) 14:579–622.[CrossRef][ISI]
  49. Yu J.-K. Smooth models associated to concave functions in Bruhat–Tits theory. (2002) preprint Advance Access 2002-20. http://www.ims.nus.edu.sg/publications-pp02.htm.

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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
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Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
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Right arrow How to cite this article
Google Scholar
Right arrow Articles by Adler, J. D.
Right arrow Articles by Spice, L.
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 Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?