Casselman, William; Shalika, J. The unramified principal series of p-adic groups. II: The Whittaker function. (English) Zbl 0472.22005 Compos. Math. 41, 207-231 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 10 ReviewsCited in 146 Documents 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 Keywords:Macdonald’s formula; zonal spherical functions on p-adic reductive group; Whittaker function; unramified principal series representation; Whittaker model; unipotent radical; parabolic subgroup; supercuspidal representation PDFBibTeX XMLCite \textit{W. Casselman} and \textit{J. Shalika}, Compos. Math. 41, 207--231 (1980; Zbl 0472.22005) Full Text: Numdam EuDML References: [1] I.N. Bernstein and A.V. Zelevinskii : Representations of the group GL(n, F) . Uspekhi Math. Nauk XXXI (1976) 5-70. · Zbl 0342.43017 [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 · doi:10.1007/BF02684396 [5] H. Jacquet , Fonctions de Whittaker associées aux groupes de Chevalley , Bull. Soc. Math. France 95 (1967), 243-309. · Zbl 0155.05901 · doi:10.24033/bsmf.1654 [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 [8] T. Shintani , On an explicit formula for class 1 Whittaker functions on GLn over P-adic fields , Proc. Japan Acad. 52 (1976), 180-182. · Zbl 0387.43002 · doi:10.3792/pja/1195518347 [9] S-I. Kato , On an explicit formula for class one Whittaker functions on classical groups over P-adic fields , preprint, Tokyo, 1978. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.