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The Knapp-Stein dimension theorem for $ p$-adic groups

Author: Allan J. Silberger
Journal: Proc. Amer. Math. Soc. 68 (1978), 243-246
MSC: Primary 22E50
Correction: Proc. Amer. Math. Soc. 76 (1979), 169-170.
MathSciNet review: 0492091
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Abstract: Knapp and Stein have proved for semisimple Lie groups that the dimension of the commuting algebra of an induced tempered representation equals the index of a certain reflection group in a larger group. A precise analogue of their result is stated and proved in this paper for p-adic groups.

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  • [1] N. Bourbaki, Éléments de mathématique, Fase. XXXIV. Groupes et algèbres de Lie, Chapters IV, V, VI, Actualités Sci. Indust., no. 1337, Hermann, Paris, 1968. MR 0240238 (39:1590)
  • [2] Harish-Chandra, Harmonic analysis on reductive p-adic groups, Proc. Sympos. Pure Math., vol. 26, Amer. Math. Soc., Providence, R. I., 1974, pp. 167-192. MR 0340486 (49:5238)
  • [3] 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 0376964 (51:13139)
  • [4] A. J. Silberger, Introduction to harmonic analysis on reductive p-adic groups, based on lectures by Harish-Chandra (to appear). MR 544991 (81m:22025)

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Keywords: Reductive p-adic groups, tempered unitary representations, commuting algebras
Article copyright: © Copyright 1978 American Mathematical Society

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