Duke Mathematical Journal

Representations of $\mathrm{GL}(n)$ and division algebras over a $p$-adic field

Jonathan D. Rogawski

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Article information

Source
Duke Math. J. Volume 50, Number 1 (1983), 161-196.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077303004

Mathematical Reviews number (MathSciNet)
MR700135

Zentralblatt MATH identifier
0523.22015

Digital Object Identifier
doi:10.1215/S0012-7094-83-05006-8

Subjects
Primary: 12B27
Secondary: 10D40 12B35 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Citation

Rogawski, Jonathan D. Representations of GL ( n ) and division algebras over a p -adic field. Duke Math. J. 50 (1983), no. 1, 161--196. doi:10.1215/S0012-7094-83-05006-8. http://projecteuclid.org/euclid.dmj/1077303004.


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References

  • [1] I. N. Bernstein and A. V. Zelevinsky, Induced representations of reductive ${\germ p}$-adic groups. I, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 4, 441–472.
  • [2] A. Borel and N. R. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies, vol. 94, Princeton University Press, Princeton, N.J., 1980.
  • [3] A. Borel, Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup, Invent. Math. 35 (1976), 233–259.
  • [4] W. Casselman, Introduction to the theory of admissible representions of $p$-adic groups, to appear.
  • [5] L. Clozel, Une démonstration de la conjecture de Howe pour le groupe linéare d'un corps $p$-adique, preprint.
  • [6] D. L. De George and N. R. Wallach, Limit formulas for multiplicities in $L\sp{2}(\Gamma \backslash G)$, Ann. Math. (2) 107 (1978), no. 1, 133–150.
  • [7] D. Flath Thesis, Harvard University, 1977.
  • [8] R. Godement and H. Jacquet, Zeta functions of simple algebras, Springer-Verlag, Berlin, 1972.
  • [9] Harish-Chandra, Admissible invariant distributions on reductive $p$-adic groups, Lie theories and their applications (Proc. Ann. Sem. Canad. Math. Congr., Queen's Univ., Kingston, Ont., 1977), Queen's Univ., Kingston, Ont., 1978, 281–347. Queen's Papers in Pure Appl. Math., No. 48.
  • [10] Harish-Chandra, Harmonic analysis on reductive $p$-adic groups, Lecture Notes in Mathematics, vol. 162, Springer-Verlag, Berlin, 1970.
  • [11] Harish-Chandra, Harmonic analysis on reductive $p$-adic groups, Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972), Amer. Math. Soc., Providence, R.I., 1973, pp. 167–192.
  • [12] R. Howe, The Fourier transform and germs of characters (case of ${\rm Gl}\sb{n}$ over a $p$-adic field), Math. Ann. 208 (1974), 305–322.
  • [13] H. Jacquet and R. P. Langlands, Automorphic forms on ${\rm GL}(2)$, Lecture Notes in Math., Springer-Verlag, Berlin, 1970.
  • [14]1 H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic representations. I, Amer. J. Math. 103 (1981), no. 3, 499–558.
  • [14]2 H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic forms. II, Amer. J. Math. 103 (1981), no. 4, 777–815.
  • [15] H. Jacquet, Generic representations, Non-commutative harmonic analysis (Actes Colloq., Marseille-Luminy, 1976), Springer, Berlin, 1977, 91–101. Lecture Notes in Math., Vol. 587.
  • [16] R. P. Langlands, Les débuts d'une formule des traces stables, to appear.
  • [17] R. P. Langlands, Base change for ${\rm GL}(2)$, Annals of Mathematics Studies, vol. 96, Princeton University Press, Princeton, N.J., 1980.
  • [18] R. Ranga Rao, Orbital integrals in reductive groups, Ann. of Math. (2) 96 (1972), 505–510.
  • [19] J. D. Rogawski, An application of the building to orbital integrals, Compositio Math. 42 (1980/81), no. 3, 417–423.
  • [20] J. Rogawski Thesis, Princeton University, 1980.
  • [21] J. A. Shalika, A theorem on semi-simple ${\cal P}$-adic groups, Ann. of Math. (2) 95 (1972), 226–242.
  • [22] M.-F. Vignéras, Caractérisation des intégrales orbitales sur un groupe réductif $p$-adique, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 3, 945–961 (1982).