On some Bruhat decomposition and the structure of the Hecke rings of p -adic Chevalley groups

Nagayoshi Iwahori; Hideya Matsumoto

Publications Mathématiques de l'IHÉS (1965)

  • Volume: 25, page 5-48
  • ISSN: 0073-8301

How to cite

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Iwahori, Nagayoshi, and Matsumoto, Hideya. "On some Bruhat decomposition and the structure of the Hecke rings of $p$-adic Chevalley groups." Publications Mathématiques de l'IHÉS 25 (1965): 5-48. <http://eudml.org/doc/103854>.

@article{Iwahori1965,
author = {Iwahori, Nagayoshi, Matsumoto, Hideya},
journal = {Publications Mathématiques de l'IHÉS},
language = {eng},
pages = {5-48},
publisher = {Institut des Hautes Études Scientifiques},
title = {On some Bruhat decomposition and the structure of the Hecke rings of $p$-adic Chevalley groups},
url = {http://eudml.org/doc/103854},
volume = {25},
year = {1965},
}

TY - JOUR
AU - Iwahori, Nagayoshi
AU - Matsumoto, Hideya
TI - On some Bruhat decomposition and the structure of the Hecke rings of $p$-adic Chevalley groups
JO - Publications Mathématiques de l'IHÉS
PY - 1965
PB - Institut des Hautes Études Scientifiques
VL - 25
SP - 5
EP - 48
LA - eng
UR - http://eudml.org/doc/103854
ER -

References

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  2. [2] R. BOTT, An application of the Morse theory to the topology of Lie groups, Bull. Soc. Math. France, 84 (1956), 251-282. Zbl0073.40001MR19,291a
  3. [3] F. BRUHAT, Sur les représentations des groupes classiques p-adiques, I, II, Amer. J. Math., 83 (1961), 321-338, 343-368. Zbl0107.02504MR23 #A3184
  4. [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. Zbl0226.20042MR31 #2352
  5. [5] E. CARTAN, La géométrie des groupes simples, Ann. Mat. Pur. Appl., 4 (1927), 209-256. Zbl53.0392.03JFM53.0392.03
  6. [6] C. CHEVALLEY, Sur certains groupes simples, Tôhoku Math. J., 7 (1955), 14-66. Zbl0066.01503MR17,457c
  7. [7] O. GOLDMAN and N. IWAHORI, The spaces of p-adic norms, Acta Math., 109 (1963), 137-177. Zbl0133.29402MR26 #2430
  8. [8] O. GOLDMAN and N. IWAHORI, On the structure of Hecke rings associated to general linear groups over p-adic fields, to appear. Zbl0133.29402
  9. [9] H. HIJIKATA, Maximal invariant orders of an involutive algebra over a local field, to appear. 
  10. [10] N. IWAHORI, On the structure of a Hecke ring of a Chevalley group over a finite field, to appear, in J. Faculty of Sci., Univ. of Tokyo, 10 (1964). Zbl0135.07101MR29 #2307
  11. [11] T. ONO, Sur les groupes de Chevalley, J. Math. Soc. Japan, 10 (1958), 307-313. Zbl0085.01705MR20 #7076
  12. [12] I. SATAKE, On spherical functions over p-adic fields, Proc. Japan Academy, 38 (1962), 422-425. Zbl0116.02303MR27 #3640
  13. [13] Séminaire "Sophus Lie", Paris, 1954-1955. 
  14. [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. Zbl0026.38603MR4,134e
  15. [15] T. TAMAGAWA, On the ζ-functions of a division algebra, Ann. of Math., 77 (1963), 387-405. Zbl0222.12018MR26 #2468
  16. [16] J. TITS, Théorème de Bruhat et sous-groupes paraboliques, C. R. Paris, 254 (1962), 2910-2912. Added in Proof. For an abstract approach to Prop. 1. 15 and its consequences see. Zbl0105.02201MR25 #2149
  17. [17] H. MATSUMOTO, Générateurs et relations des groupes de Weyl généralisés, to appear. Zbl0128.25202

Citations in EuDML Documents

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  1. Bao Chau Ngô, Alain Genestier, Alcôves et p -rang des variétés abéliennes
  2. Nanhua Xi, The based ring of the lowest two-sided cell of an affine Weyl group. II
  3. W. Casselman, J. Shalika, The unramified principal series of p -adic groups. II. The Whittaker function
  4. François Bruhat, Sous-groupes compacts maximaux des groupes semi-simples p -adiques
  5. A. Connes, Indice des sous facteurs, algèbres de Hecke et théorie des noeuds
  6. Xuhua He, Thomas Lam, [unknown]
  7. Howard Garland, The arithmetic theory of loop groups
  8. Calvin C. Moore, Group extensions of p -adic and adelic linear groups
  9. Hervé Jacquet, Fonctions de Whittaker associées aux groupes de Chevalley
  10. François Rodier, Sur les représentations non ramifiées des groupes réductifs p -adiques ; l’exemple de G S p ( 4 )

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