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On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups. (English) Zbl 0228.20015

MSC:
20E28Maximal subgroups of groups
References:
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[2]R. Bott, An application of the Morse theory to the topology of Lie groups,Bull. Soc. Math. France, 84 (1956), 251–282.
[3]F. Bruhat, Sur les représentations des groupes classiques p-adiques, I, II,Amer. J. Math., 83 (1961), 321–338, 343–368. · Zbl 0107.02504 · doi:10.2307/2372958
[4]F. Bruhat, Sur les sous-groupes compacts maximaux des groupes semi-simples p-adiques,Colloque sur la théorie des groupes algébriques, Bruxelles (1962), 69–76.
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[8]O. Goldman andN. Iwahori,On the structure of Hecke rings associated to general linear groups over p-adic fields, to appear.
[9]H. Hijikata,Maximal invariant orders of an involutive algebra over a local field, to appear.
[10]N. Iwahori, On the structure of a Hecke ring of a Chevalley group over a finite field, to appear, inJ. Faculty of Sci., Univ. of Tokyo, 10 (1964).
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[12]I. Satake, On spherical functions over p-adic fields,Proc. Japan Academy, 38 (1962), 422–425. · Zbl 0116.02303 · doi:10.3792/pja/1195523281
[13]Séminaire “Sophus Lie ”, Paris, 1954–1955.
[14]E. Stiefel, Über eine Beziehung zwischen geschlossenen Lieschen Gruppen und diskontinuierlichen Bewegungsgruppen euklidischer Räume und ihre Anwendung auf die Aufzählung der einfachen Lie’schen Gruppen,Comm. Math. Helv., 14 (1941), 350–379. · Zbl 0026.38603 · doi:10.1007/BF02565625
[15]T. Tamagawa, On the ζ-functions of a division algebra,Ann. of Math., 77 (1963), 387–405. · Zbl 0222.12018 · doi:10.2307/1970221
[16]J. Tits, Théorème de Bruhat et sous-groupes paraboliques,C. R. Paris, 254 (1962), 2910–2912.