The Knapp-Stein dimension theorem for $p$-adic groups
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- by Allan J. Silberger PDF
- Proc. Amer. Math. Soc. 68 (1978), 243-246 Request permission
Correction: Proc. Amer. Math. Soc. 76 (1979), 169-170.
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.References
- N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- 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
- 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
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 243-246
- MSC: Primary 22E50
- DOI: https://doi.org/10.1090/S0002-9939-1978-0492091-5
- MathSciNet review: 0492091