Any unitary principal series representation of $(GL)_{n}$ over a $p$-adic field is irreducible
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- by Roger Howe and Allan Silberger PDF
- Proc. Amer. Math. Soc. 54 (1976), 376-378 Request permission
Abstract:
This paper proves that for the group ${\operatorname {GL} _n}$ over the $p$-adics every unitary principal series representation is irreducible.References
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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.
β, Notes on lectures at the Institute for Advanced Study, 1971-1973 (to appear).
- Roger Howe and Allan Silberger, Why any unitary principal series representation of $\textrm {SL}_n$ over a $p$-adic field decomposes simply, Bull. Amer. Math. Soc. 81 (1975), 599β601. MR 369623, DOI 10.1090/S0002-9904-1975-13750-5
- George W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265β311. MR 98328, DOI 10.1007/BF02392428 F. I. Mautner, Spherical functions over $\mathfrak {P}$-adic fields. I, II, Amer. J. Math. 80 (1958), 441-457; ibid, 86 (1964), 171-200. MR 20 #82; 29 #3582.
- Allan J. Silberger, $\textrm {PGL}_{2}$ over the $p$-adics: its representations, spherical functions, and Fourier analysis, Lecture Notes in Mathematics, Vol. 166, Springer-Verlag, Berlin-New York, 1970. MR 0285673, DOI 10.1007/BFb0059369
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 376-378
- MSC: Primary 22E50
- DOI: https://doi.org/10.1090/S0002-9939-1976-0422521-4
- MathSciNet review: 0422521