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Reducibility of unramified unitary principal series representations of p- adic groups and class-1 representations. (English) Zbl 0488.22026

MSC:
22E46 Semisimple Lie groups and their representations
22E35 Analysis on \(p\)-adic Lie groups
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References:
[1] Bruhat, F., Tits, J.: Groupes reductifs sur un corps local. Publ. I.H.E.S.41, 5-252 (1972)
[2] Keys. D.: On the decomposition of reducible principal series representations ofp-adic Chevalley groups (to appear in Pacific J.) · Zbl 0438.22010
[3] Knapp, A.W., Stein, E.M.: Interwining operators for semi-simple groups. II. Inventiones Math.60, 9-84 (1980) · Zbl 0454.22010
[4] MacDonald, I.G.: Spherical functions on a group ofp-adic type. Ramanujan Institute, University of Madras, Madras, India, 1972
[5] Satake, I.: Theory of spherical functions on reductive algebraic groups overp-adic fields. Publ. I.H.E.S.18, 5-70 (1963)
[6] Silberger, A.: Introduction to harmonic analysis on reductivep-adic groups. Math. Notes, Vol. 23. Princeton, NJ: Princeton University Press 1979 · Zbl 0458.22006
[7] Silberger, A.: The Knapp-Stein dimension theorem forp-adic groups (to appear) · Zbl 0415.22020
[8] Tits, J.: Reductive groups over local fields. In: Automorphic forms, representations andL-functions. Providence: American Mathematical Society 1979 · Zbl 0415.20035
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