On representation theory of symmetric groups
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IX, Tome 301 (2003), pp. 229-242 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We present here a new approach to description of finite-dimensional complex irreducible representations of symmetric groups due to A. Okounkov and A. Vershik. It gives an alternative construction to the combinatorial one using tabloids, polytabloids and Specht modules. Its aim is to show how the combinatorial objects of the theory (Young diagrams and tableaux) come from the inside structure of the symmetric group.
@article{ZNSL_2003_301_a8,
     author = {P. Py},
     title = {On representation theory of symmetric groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {229--242},
     year = {2003},
     volume = {301},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_301_a8/}
}
TY  - JOUR
AU  - P. Py
TI  - On representation theory of symmetric groups
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 229
EP  - 242
VL  - 301
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_301_a8/
LA  - en
ID  - ZNSL_2003_301_a8
ER  - 
%0 Journal Article
%A P. Py
%T On representation theory of symmetric groups
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 229-242
%V 301
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_301_a8/
%G en
%F ZNSL_2003_301_a8
P. Py. On representation theory of symmetric groups. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IX, Tome 301 (2003), pp. 229-242. http://geodesic.mathdoc.fr/item/ZNSL_2003_301_a8/

[1] P. Diaconis, “Application of noncommutative Fourier analysis to probability problems”, Ecole d'été de probabilités de Saint-Flour, XV–XVII (1985–1987), Lecture Notes in Math., 1362, ed. P. L. Hennequin, Springer-Verlag, 1988, 51–100 | MR

[2] A. Okounkov, A. Vershik, “A new approach to representation theory of symmetric groups”, Selecta Math., New Ser., 2 (1996), 581–605 | DOI | MR | Zbl

[3] J. Friedman, “On Cayley graphs on the symmetric group generated by transpositions”, Combinatorica, 20 (2000), 505–519 | DOI | MR | Zbl

[4] J. Friedman, P. Hanlon, “On the Betti numbers of chessboard complexes”, J. Algebraic Combin., 8 (1996), 193–203 | DOI | MR

[5] A. M. Odlyzko, L. Flatto, D. B. Wales, “Random shuffles and group representation”, Ann. Probab., 13 (1985), 587–598 | DOI | MR

[6] G. I. Olshanski, “Extension of the algebra $U(g)$ for infinite-dimensional classical Lie algebras $g$ and the Yangians $Y(gl(m))$”, Soviet. Math. Dokl., 36 (1988), 569–573 | MR

[7] B. Sagan, The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edition, Springer, 2000 | MR

[8] F. Scarabotti, “Radon transforms on the symmetric group and harmonic analysis of a class of invariant Laplacians”, Forum Math., 10 (1998), 407–411 | DOI | MR | Zbl

[9] J.-P. Serre, Représentations Linéaires des Groupes Finis, Hermann, 1967 | MR | Zbl