Kato, Shin-ichi On eigenspaces of the Hecke algebra with respect to a good maximal compact subgroup of a p-adic reductive group. (English) Zbl 0452.43014 Math. Ann. 257, 1-7 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 12 Documents 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 Keywords:eigenfunctions of invariant differential operators; p-adic reductive group; Hecke algebra; p-adic Poisson integrals Citations:Zbl 0377.43012 PDFBibTeX XMLCite \textit{S.-i. Kato}, Math. Ann. 257, 1--7 (1981; Zbl 0452.43014) Full Text: DOI EuDML 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 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.