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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Complementary series for $p$-adic groups. I
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by Allan J. Silberger PDF
Trans. Amer. Math. Soc. 259 (1980), 589-598 Request permission


Let $\Omega$ be a nonarchimedean local field, G the group of $\Omega$-points of a connected reductive algebraic group defined over $\Omega$. This paper establishes that to each zero of the Plancherel measure of G one can associate complementary series. Our result is the analogue for p-adic groups of a similar statement, announced separately by Knapp-Stein and Harish-Chandra, for real groups.
  • I. M. Gel′fand and M. I. Graev, Representations of the group of second-order matrices with elements in a locally compact field and special functions on locally compact fields, Uspehi Mat. Nauk 18 (1963), no. 4 (112), 29–99 (Russian). MR 0155931
  • Harish-Chandra, On the theory of the Eisenstein integral, Conference on Harmonic Analysis (Univ. Maryland, College Park, Md., 1971), Lecture Notes in Math., Vol. 266, Springer, Berlin, 1972, pp. 123–149. MR 0399355
  • 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. MR 0340486
  • A. W. Knapp and E. M. Stein, Singular integrals and the principal series. IV, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), 2459–2461. MR 376964, DOI 10.1073/pnas.72.6.2459
  • R. G. Laha, Complementary series representations of ${\text {GL}}(2,\,D)$, where D is a central division algebra over a non-archimedean local field, Notices Amer. Math. Soc. 25 (1978), p. A-262; Abstract #753-B44.
  • G. I. Ol′šanskiĭ, Intertwining operators and complementary series in the class of representations of the full matrix group over a locally compact division algebra that are induced by parabolic subgroups, Mat. Sb. (N.S.) 93(135) (1974), 218–253, 326 (Russian). MR 0499010
  • Allan J. Silberger, Introduction to harmonic analysis on reductive $p$-adic groups, Mathematical Notes, vol. 23, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1979. Based on lectures by Harish-Chandra at the Institute for Advanced Study, 1971–1973. MR 544991
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 259 (1980), 589-598
  • MSC: Primary 22E50
  • DOI:
  • MathSciNet review: 567099