Casselman, William The unramified principal series of p-adic groups. I: The spherical function. (English) Zbl 0472.22004 Compos. Math. 40, 387-406 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 118 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:unramified principal series; zonal spherical functions on p-adic reductive groups; intertwining operators; Jacquet modules; reductive group over global field; Macdonald’s formula Citations:Zbl 0273.22012; Zbl 0366.22001 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML References: [1] A. Borel : Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup . Inventiones Math. 35 (1976) 233-259. · Zbl 0334.22012 · doi:10.1007/BF01390139 [2] A. Borel and J. Tits : Groupes réductifs , Publ. Math. I.H.E.S. 27 (1965) 55-151. · Zbl 0145.17402 · doi:10.1007/BF02684375 [3] A. Borel and J. Tits : Compléments à l’article ”Groupes.réductifs” , Publ. Math. I.H.E.S. 41 (1972) 253-276. · Zbl 0254.14018 · doi:10.1007/BF02715545 [4] A. Borel and J. Tits : Homomorphismes ”abstraits” de groupes algebriques simples . Annals of Math. 97 (1973) 499-571. · Zbl 0272.14013 · doi:10.2307/1970833 [5] N. Bourbaki : Groupes et algèbres de Lie . Chapitres IV, V, et VI. Hermann, Paris, 1968. · Zbl 0186.33001 [6] F. Bruhat and J. Tits : Groupes réductifs sur un corps local , Publ. Math. I.H.E.S. 41 (1972) 1-251. · Zbl 0254.14017 · doi:10.1007/BF02715544 [7] W. Casselman : Introduction to the theory of admissible representations of p-adic reductive groups (to appear). [8] N. Iwahori : Generalized Tits systems on p-adic semi-simple groups, in Algebraic Groups and Discontinuous Subgroups . Proc. Symp. Pure Math. IX. A.M.S., Providence, 1966. · Zbl 0199.06901 [9] I.G. Macdonald : Spherical functions on a p-adic Chevalley group . Bull. Amer. Math. Soc. 74 (1968) 520-525. · Zbl 0273.22012 · doi:10.1090/S0002-9904-1968-11989-5 [10] I.G. Macdonald : Spherical functions on a group of p-adic type . University of Madras, 1971. · Zbl 0302.43018 [11] R. Steinberg : Lectures on Chevalley groups . Yale University Lecture Notes, 1967. · Zbl 1361.20003 · doi:10.1090/ulect/066 [12] H. Matsumoto : Analyse Harmonique dans les Système de Tits Bomologiques de Type Affine . Springer Lecture Notes#590, Berlin, 1977. · Zbl 0366.22001 [13] J. Tits : Reductive groups over local fields . Proc. Symp. Pure Math. XXXIII, Amer. Math. Soc., Providence, 1978. · Zbl 0415.20035 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.