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Classification of the primitive representations of the Galois group of local fields. (English) Zbl 0376.12003


MSC:

11R32 Galois theory
11R52 Quaternion and other division algebras: arithmetic, zeta functions
20C25 Projective representations and multipliers
11S20 Galois theory
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References:

[1] Curtis, C.W., Reiner, I.: Representation theory. New York-London: Interscience 1962 · Zbl 0131.25601
[2] Diendonné, J.: La géométrie des groupes classiques, 3rd ed. Berlin-Heidelberg-New York: Springer 1971
[3] Hasse, H.: Zahlentheorie, 2. Aufl. Berlin: Akademie Verlag 1963 · Zbl 0107.24805
[4] Iwasawa, K.: On Galois groups of local fields. Trans. Am. Math. Soc.80, 448-469 (1955) · Zbl 0074.03101 · doi:10.1090/S0002-9947-1955-0075239-5
[5] Kamenski, A.G.: On the representations of theW-group of a local field (Russian). Uspechi mat. Nauk30, 245-250 (1975)
[6] Koch, H.: Die irreduziblen Darstellungen von Primzahlgrad der Galoisschen Gruppe eines lokalen Körpers. Klassenberichte d. Akademie d. Wissenschaften d. DDR 18N, 59-70 (1976)
[7] Krasner, M.: Sur la representation exponentielle dans les corps relativement galoisiens de nombres ?-adiques. Acta Arithmetica3, 133-173 (1939) · JFM 65.0113.01
[8] Pieper, H.: Die Einheitengruppe eines zahmverzweigten galoisschen lokalen Körpers als Galois-Modul. Math. Nachr.54, 173-210 (1972) · Zbl 0263.12009 · doi:10.1002/mana.19720540113
[9] Rigby, J.F.: Primitive linear groups containing a normal nilpotent subgroup larger than the centre of the group. J. London Math. Soc.35, 389-400 (1960) · Zbl 0096.25205 · doi:10.1112/jlms/s1-35.4.389
[10] Serre, J-P.: Cohomologie Galoisienne. Lecture Notes in Math. 5. Berlin-Heidelberg-New York: Springer 1964 · Zbl 0143.05901
[11] Serre, J-P.: Representation lineaires des group finis. Paris: Hermann 1967
[12] Suprunenko, D.A.: Matrix groups. Nauka, Moscow 1972 (Russian)
[13] Weil, A.: Exercises dyadiques. Inventiones math.27, 1-22 (1974) · Zbl 0307.12017 · doi:10.1007/BF01389962
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