Bulletin of the American Mathematical Society

Why any unitary principal series representation of $SL_n$ over a $p$-adic field decomposes simply

Roger Howe and Allan Silberger

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Bull. Amer. Math. Soc., Volume 81Number 3, Part 1 (1975), 599-601.

First available in Project Euclid: 4 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Secondary: 22E35: Analysis on $p$-adic Lie groups 22D10: Unitary representations of locally compact groups 22D30: Induced representations


Howe, Roger; Silberger, Allan. Why any unitary principal series representation of $SL_n$ over a $p$-adic field decomposes simply. Bull. Amer. Math. Soc. 81 (1975), 599--601. https://projecteuclid.org/euclid.bams/1183536881

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  • 1. R. Howe, The Fourier transform and germs of characters (Case of GLn over a p-adic field), Math. Ann. 208 (1974), 305-322.
  • 2. R. Howe and A. Silberger, Any unitary principal series representation of GLn over a p-adic field is irreducible, Proc. Amer. Math. Soc. (to appear).
  • 3. A. Knapp, Commutativity of intertwining operators, Bull. Amer. Math. Soc. 79 (1973), 1016-1018.
  • 4. F. Rodier, Whittaker models for admissible representations of reductive p-adic split groups, Proc. Sympos. Pure Math., vol. 26, Amer. Math. Soc., Providence, R. I., 1974, pp. 425-430.
  • 5. F. Rodier, Modèles de Whittaker et caractères de représentations (preprint).