La théorie classique et moderne des fonctions symétriques
Séminaire Bourbaki (1982-1983)
- Volume: 25, page 1-23
- ISSN: 0303-1179
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topCartier, Pierre. "La théorie classique et moderne des fonctions symétriques." Séminaire Bourbaki 25 (1982-1983): 1-23. <http://eudml.org/doc/110008>.
@article{Cartier1982-1983,
author = {Cartier, Pierre},
journal = {Séminaire Bourbaki},
keywords = {representations of symmetric groups; survey; symmetric functions; generating series; partitions; symmetric formal power series; Hopf bigebra; general linear groups},
language = {fre},
pages = {1-23},
publisher = {Société Mathématique de France},
title = {La théorie classique et moderne des fonctions symétriques},
url = {http://eudml.org/doc/110008},
volume = {25},
year = {1982-1983},
}
TY - JOUR
AU - Cartier, Pierre
TI - La théorie classique et moderne des fonctions symétriques
JO - Séminaire Bourbaki
PY - 1982-1983
PB - Société Mathématique de France
VL - 25
SP - 1
EP - 23
LA - fre
KW - representations of symmetric groups; survey; symmetric functions; generating series; partitions; symmetric formal power series; Hopf bigebra; general linear groups
UR - http://eudml.org/doc/110008
ER -
References
top- [1] D. Foata (éditeur) - Combinatoire et représentation du groupe symétrique, Lecture Notes in Math. vol. 579, Springer-Verlag, 1977. Zbl0342.00005MR466293
- [2] G. Andrews - The theory of partitions, Encycl. of Math. vol. 2, Addison-Wesley, 1976. Zbl0655.10001
- [3] W. Bailey - Generalized hypergeometric functions, Cambridge Univ. Press, 1964 (2e édition).
- [4] N. Bourbaki - Algèbre, chapitres 4 à 7, Masson, 1981. Zbl0498.12001MR643362
- [5] G. James et A. Kerber - The representation theory of the symmetric group, Encycl. of Math. vol. 16, Addison-Wesley, 1981. Zbl0491.20010MR644144
- [6] D. Knuth - The art of computer programming, vol. 3 ("Sorting and searching"), Addison-Wesley, 1975. Zbl0883.68015MR378456
- [7] D. Knutson - λ-rings and the representation theory of symmetric groups, Lecture Notes in Math. vol. 380, Springer-Verlag, 1973. Zbl0272.20008
- [8] J.E. Littlewood - The theory fo group characters and matrix representations of groups, Oxford, 1950 (2e édition). Zbl0038.16504
- [9] I.G. Macdonald - Symmetric functions and Hall polynomials, OxfordUniversity Press, 1979. Zbl0899.05068MR553598
- [10] P. Macmahon - Combinatory Analysis, 2 volumes, Cambridge University Press, 1915/16 (réimprimé par Chelsea, 1960). MR141605JFM46.0118.07
- [11] P. Macmahon - Collected Papers, vol. 1, M.I.T. Press, 1978. Zbl0557.01015MR514405
- [12] F. Murnaghan - The theory of group representations, Dover Publ., 1963 (réimpression). Zbl0131.02701MR175982
- [13] G. de B. Robinson - Representation theory of the symmetric group, University of Toronto Press, 1961. Zbl0102.02002MR125885
- [14] H. Weyl - The classical groups, their invariants and representations, Princeton University Press, 1939. MR1488158JFM65.0058.02
- [15] A. Young - Collected Papers, University of Toronto Press, 1977. Zbl0362.01007MR439548
- [16] A. Zelevinsky - Representations of finite classical groups (A Hopf approach), Lecture Notes in Math. vol. 869, Springer-Verlag, 1981. Zbl0465.20009MR643482
- [17] D. Foata et M.P. Schützenberger - Théorie géométrique des polynômes eulériens, Lecture Notes in Math. vol. 138, Springer-Verlag, 1970. Zbl0214.26202MR272642
- [18] P. Doubilet - On the foundations of combinatorial theory VII : Symmetric functions through the theory of distribution and occupancy, Studies in Appl. Math.51(1972), 377-396. Zbl0274.05008MR429577
- [19] J. Désarmenien - Fonctions symétriques associées à des suites classiques de nombres, Annales Sci. E.N.S.16(1983), Zbl0525.05006MR732346
- [20] I. Schur - Über eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen, in Gesammelte Abhandlungen, tome 1, p. 1-70, Springer-Verlag, 1973. JFM32.0165.04
- [21] P. Hoffman - τ-rings and wreath product representations, Lecture Notes in Math. vol. 746, Springer-Verlag, 1979. Zbl0443.55013
- [22] A. Lascoux - Classes de Chern d'un produit tensoriel, Comptes Rendus Acad. Sci. Paris t. 286, série A(1978), 385-387. Zbl0379.55011MR476745
- [23] J. Green - The characters of the finite general linear group, Trans. Amer. Math. Soc. 80(1955), 402-447. Zbl0068.25605MR72878
- [24] D.K. Faddeev - The complex representations of the general linear group over a finite field, Zapiski Nauchn. LOMI, 46(1974), 64-88. Zbl0346.20024MR382417
- [25] S.V. Nagornyi - Complex representations of classical groups over a finite field, Zapiski Nauchn. LOMI, 86(1979), 135-156. Zbl0433.20034MR535486
- [26] A. Lascoux et M.P. Schützenberger - Le monoïde plaxique, in Noncommutative structures in algebra and geometric combinatories, p. 129-156, Quaderni Ricerca Scientifica n° 109, 1981. Zbl0517.20036MR646486
- [27] H.O. Foulkes - Eulerian numbers, Newcomb's problem and representations of symmetric groups, Discrete Math.30(1980), 3-49. Zbl0445.05008MR561763
- [28] A. Lascoux - Classes de Chern des variétés de drapeaux, Comptes rendus Acad.Sci. Paris t. 295, série I(1982), 393-398. Zbl0495.14032MR684734
- [29] P. Cartier - Groupes formels, représentations des groupes symétriques et congruences de Kummer, Sém. Théorie des Nombres, Paris1982-83, à paraître dans Progress in Math., Birkhäuser.
- [30] G. Baster - An analytic problem whose solution follows from a simple algebraic identity, Pac. Journ. Math.10(1960), 731-742. Zbl0095.12705MR119224
- [31] P. Cartier - La série génératrice exponentielle, Publication I.R.M.A., Strasbourg, 1972.
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