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On eigenspaces of the Hecke algebra with respect to a good maximal compact subgroup of a p-adic reductive group. (English) Zbl 0452.43014


MSC:

43A85 Harmonic analysis on homogeneous spaces
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
11R56 Adèle rings and groups
22E35 Analysis on \(p\)-adic Lie groups

Citations:

Zbl 0377.43012
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References:

[1] Borel, A.: Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup. Invent. Math.35, 223-259 (1976) · Zbl 0334.22012 · doi:10.1007/BF01390139
[2] Bruhat, F., Tits, J.: Groupes réductifs sur un corps local. Chap. I. Publ. Math. I.H.E.S.41, 1-251 (1972) · Zbl 0254.14017
[3] Kashiwara, M., Kowata, A., Minemura, K., Okamoto, K., Oshima, T., Tanaka, M.: Eigenfunctions of invariant differential operators on a symmetric space. Ann. Math.107, 1-39 (1978) · Zbl 0377.43012 · doi:10.2307/1971253
[4] Macdonald, I.G.: Spherical functions on a group ofp-adic type. Publ. Ramanujan Institute. No. 2. Madras (1971) · Zbl 0302.43018
[5] Matsumoto, H.: Analyse harmonique dans les systèmes de Tits bornologiques de type affine. Lecture Notes in Mathematics, Vol. 590. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0366.22001
[6] Satake, I.: Theory of spherical functions on reductive algebraic groups overp-adic fields. Publ. Math. I.H.E.S.18, 5-69 (1963)
[7] Steinberg, R.: Differential equations invariant under finite reflection groups. Trans. Am. Math. Soc.112, 392-400 (1964) · Zbl 0196.39202 · doi:10.1090/S0002-9947-1964-0167535-3
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