Un peu d’histoire des groupes finis et quelques exemples simples

Aubert, Anne-Marie

Journées mathématiques X-UPS, Groupes finis (2000), pp. 1-56.

[ABFS99] Aschbacher, Michael; Bender, Helmut; Feit, Walter; Solomon, Ronald Michio Suzuki (1926–1998), Notices Amer. Math. Soc., Volume 46 (1999) no. 5, pp. 543-551 | MR

[AMR96] Aubert, Anne-Marie; Michel, Jean; Rouquier, Raphaël Correspondance de Howe pour les groupes réductifs sur les corps finis, Duke Math. J., Volume 83 (1996) no. 2, pp. 353-397 | DOI | Zbl

[Art55a] Artin, Emil The orders of the classical simple groups, Comm. Pure Appl. Math., Volume 8 (1955), pp. 455-472 | DOI | MR | Zbl

[Art55b] Artin, Emil The orders of the linear groups, Comm. Pure Appl. Math., Volume 8 (1955), pp. 355-365 | DOI | MR | Zbl

[Art96] Artin, Emil Algèbre géométrique, Les Grands Classiques Gauthier-Villars, Éditions Jacques Gabay, Paris, 1996 (Traduction par M. Lazard de l’édition originale en anglais de 1957. Réédition de l’édition française de 1962)

[Aub03] Aubert, Anne-Marie Character sheaves and generalized Springer correspondence, Nagoya Math. J., Volume 170 (2003), pp. 47-72 | DOI | MR | Zbl

[Bur55] Burnside, W. Theory of groups of finite order, Dover Publications, Inc., New York, 1955 (1^re éd. en 1911) | MR

[Car56] Carmichael, Robert D. Introduction to the theory of groups of finite order, Dover Publications, Inc., New York, 1956 | MR

[Car89] Carter, Roger W. Simple groups of Lie type, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1989 | MR

[Che55] Chevalley, Claude Sur certains groupes simples, Tohoku Math. J. (2), Volume 7 (1955), pp. 14-66 | DOI | MR | Zbl

[Che97] Chevalley, Claude The algebraic theory of spinors and Clifford algebras, Springer-Verlag, Berlin, 1997 (Collected works. Vol. 2, Columbia University Press, New York, 1954)

[Con69a] Conway, J. H. A characterisation of Leech’s lattice, Invent. Math., Volume 7 (1969), pp. 137-142 | DOI | MR | Zbl

[Con69b] Conway, J. H. A group of order $8,315,553,613,086,720,000$, Bull. London Math. Soc., Volume 1 (1969), pp. 79-88 | DOI | MR | Zbl

[Dic01] Dickson, Leonard Eugene Theory of linear groups in an arbitrary field, Trans. Amer. Math. Soc., Volume 2 (1901) no. 4, pp. 363-394 Errata : Ibid. 3 (1902), no. 4, p. 500 | DOI | MR

[Dic02] Dickson, Leonard Eugene A class of groups in an arbitrary realm connected with the configuration of the 27 lines on a cubic surface, Q. J. Math., Volume 33 (1902), pp. 145-173 | Zbl

[Dic05] Dickson, Leonard Eugene A new system of simple groups, Math. Ann., Volume 60 (1905), pp. 137-150 | DOI | MR

[Dic07] Dickson, Leonard Eugene A class of groups in an arbitrary realm connected with the configuration of the 27 lines on a cubic surface, II, Q. J. Math., Volume 39 (1907), pp. 205-209 | Zbl

[Dic58] Dickson, Leonard Eugene Linear groups : With an exposition of the Galois field theory, Dover Publications, Inc., New York, 1958 (Réédition de l’édition originale de 1901)

[Die71] Dieudonné, Jean A. La géométrie des groupes classiques, Ergeb. Math. Grenzgeb. (3), 5, Springer-Verlag, Berlin-New York, 1971 | MR

[Ema89] Emaldi, Maurizio Giovanni Frattini 1852–1925, Irish Math. Soc. Bull. (1989) no. 23, pp. 57-61 | DOI | MR | Zbl

[FH91] Fulton, William; Harris, Joe Representation theory. A first course, Graduate Texts in Math., 129, Springer-Verlag, New York, 1991 | DOI

[Ful97] Fulton, William Young tableaux. With applications to representation theory and geometry, London Math. Soc. Student Texts, 35, Cambridge University Press, Cambridge, 1997

[Gor68] Gorenstein, Daniel Finite groups, Harper & Row, Publishers, New York-London, 1968

[Gér77] Gérardin, Paul Weil representations associated to finite fields, J. Algebra, Volume 46 (1977) no. 1, pp. 54-101 | DOI | MR | Zbl

[How73] Howe, Roger Invariant theory and duality for classical groups over finite fields, with applications to their singular representation theory (1973) (Preprint, Yale Univ.)

[Hup67] Huppert, B. Endliche Gruppen. I, Grundlehren Math. Wissen., 134, Springer-Verlag, Berlin-New York, 1967 | DOI

[Jac75] Jacobson, Nathan Lectures in abstract algebra, Graduate Texts in Math., 30–32, Springer-Verlag, New York-Berlin, 1975

[Jac85] Jacobson, Nathan Basic algebra. I, W. H. Freeman and Company, New York, 1985

[Jam78] James, Gordon The representation theory of the symmetric groups, Lect. Notes in Math., 682, Springer, Berlin, 1978 | Numdam

[JK81] James, Gordon; Kerber, Adalbert The representation theory of the symmetric group, Encyclopedia of Mathematics and its applications, 16, Addison-Wesley Publishing Co., Reading, Mass., 1981

[Jor89] Jordan, Camille Traité des substitutions et des équations algébriques, Les Grands Classiques Gauthier-Villars, Éditions Jacques Gabay, Sceaux, 1989 (Réédition de l’édition originale de 1870)

[Kir74] Kirillov, A. Éléments de la théorie des représentations, Éditions Mir, Moscou, 1974 | MR

[KM90] Kastler, D.; Mebkhout, M. Revisiting the Mackey-Stone-von Neumann theorem : the $C^{*}$-algebra of a presymplectic space, Nuclear Phys. B Proc. Suppl., Volume 18B (1990), pp. 200-211 Recent advances in field theory (Annecy-le-Vieux, 1990) | DOI | MR | Zbl

[Lee67] Leech, John Notes on sphere packings, Canad. J. Math., Volume 19 (1967), pp. 251-267 | DOI | MR | Zbl

[LV80] Lion, Gérard; Vergne, Michèle The Weil representation, Maslov index and theta series, Progress in Math., 6., Birkhäuser, Boston, Mass., 1980 | DOI

[Mac89] Mackey, George W. Marshall Harvey Stone. 1903–1989, Notices Amer. Math. Soc., Volume 36 (1989) no. 3, pp. 221-223 | MR | Zbl

[Mat61] Mathieu, Émile Mémoire sur l’étude des fonctions de plusieurs quantités, sur la manière de les former et sur les substitutions qui les laissent invariables, J. Math. Pures Appl., Volume 6 (1861), pp. 241-323 | Numdam

[Mat73] Mathieu, Émile Sur la fonction cinq fois transitive de 24 quantités, J. Math. Pures Appl., Volume 18 (1873), pp. 25-46 | Numdam | Zbl

[MVW87] Mœglin, Colette; Vignéras, Marie-France; Waldspurger, Jean-Loup Correspondances de Howe sur un corps $p$-adique, Lect. Notes in Math., 1291, Springer-Verlag, Berlin, 1987 | DOI

[Neu02] Neuhauser, Markus An explicit construction of the metaplectic representation over a finite field, J. Lie Theory, Volume 12 (2002) no. 1, pp. 15-30 | MR | Zbl

[Par89] Parshall, Karen Hunger Eliakim Hastings Moore and the founding of a mathematical community in America, 1892–1902, A century of mathematics in America, Part II (Hist. Math.), Volume 2, American Mathematical Society, Providence, RI, 1989, pp. 155-175 | MR | Zbl

[Par91] Parshall, Karen Hunger A study in group theory : Leonard Eugene Dickson’s Linear groups, Math. Intelligencer, Volume 13 (1991) no. 1, pp. 7-11 | DOI | MR | Zbl

[PSA96] Pantoja, José; Soto-Andrade, Jorge Représentations de Weil de ${\mathrm{SL}}_{*}(2,A)$ et $\mathrm{SL}(n,q)$, C. R. Acad. Sci. Paris Sér. I Math., Volume 323 (1996) no. 10, pp. 1109-1112 | Zbl

[Rot95] Rotman, Joseph J. An introduction to the theory of groups, Graduate Texts in Math., 148, Springer-Verlag, New York, 1995 | DOI

[Sag01] Sagan, Bruce E. The symmetric group. Representations, combinatorial algorithms, and symmetric functions., Graduate Texts in Math., 203, Springer, New York, NY, 2001

[Sco87] Scott, W. R. Group theory, Dover Publications, Inc., New York, 1987

[Ser78] Serre, Jean-Pierre Représentations linéaires des groupes finis, Hermann, Paris, 1978

[Ser99] Serre, Jean-Pierre La vie et l’œuvre d’André Weil, Enseign. Math. (2), Volume 45 (1999) no. 1-2, pp. 5-16 | Zbl

[Sha62] Shale, David Linear symmetries of free boson fields, Trans. Amer. Math. Soc., Volume 103 (1962), pp. 149-167 | DOI | MR | Zbl

[Suz60] Suzuki, Michio A new type of simple groups of finite order, Proc. Nat. Acad. Sci. U.S.A., Volume 46 (1960), pp. 868-870 | DOI | MR | Zbl

[vN96] von Neumann, John Mathematische Grundlagen der Quantenmechanik, Springer, Berlin, 1996 | DOI

[Wag78] Wagner, Ascher A bibliography of William Burnside (1852–1927), Historia Math., Volume 5 (1978) no. 3, pp. 307-312 | DOI | MR | Zbl

[Wal77] Wallach, Nolan R. Symplectic geometry and Fourier analysis, Lie Groups : History, Frontiers and Applications, V., Math Sci Press, Brookline, Mass., 1977

[Wal01] Waldspurger, Jean-Loup Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés, Astérisque, 269, Société Mathématique de France, Paris, 2001 | Numdam

[Wei64] Weil, André Sur certains groupes d’opérateurs unitaires, Acta Math., Volume 111 (1964), pp. 143-211 | DOI | Zbl

[Wey39] Weyl, Hermann The classical groups. Their invariants and representations, Princeton University Press, Princeton, NJ, 1939

[Zel81] Zelevinsky, Andrey V. Representations of finite classical groups. A Hopf algebra approach, Lect. Notes in Math., 869, Springer-Verlag, Berlin-New York, 1981 | MR