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The unramified principal series of p-adic groups. II: The Whittaker function. (English) Zbl 0472.22005

MSC:
22E50 Representations of Lie and linear algebraic groups over local fields
22E35 Analysis on \(p\)-adic Lie groups
11R39 Langlands-Weil conjectures, nonabelian class field theory
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
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References:
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[2] W. Casselman , Introduction to the theory of admissible representations of P-adic groups (to appear). · Zbl 0472.22004
[3] W. Casselman : The unramified principal series of P-adic groups I. The spherical function . Comp. Math. (1980). · Zbl 0472.22004
[4] N. Iwahori and H. Matsumoto : On some Bruhat decomposition.... , Publ. Math. I.H.E.S. 25 (1965), 5-48. · Zbl 0228.20015
[5] H. Jacquet , Fonctions de Whittaker associées aux groupes de Chevalley , Bull. Soc. Math. France 95 (1967), 243-309. · Zbl 0155.05901
[6] F. Rodier , Whittaker models for admissible representations of reductive P-adic split groups, in Harmonic Analysis on Homogeneous Spaces , Proc. Symp. Pure Math. XXVI, Amer. Math. Soc., 1973. · Zbl 0287.22016
[7] F. Shahidi , The functional equation satisfied by certain L-functions , Comp. Math. 37 (1978), 171-208. · Zbl 0393.12017
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[9] S-I. Kato , On an explicit formula for class one Whittaker functions on classical groups over P-adic fields , preprint, Tokyo, 1978.
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