2005/03/31 by A. M. Vershik, A. Yu. Okounkov
Mathematics · #math.RT #math.QA #msc:05E05 #msc:81R05
published as Zapiski Seminarod POMI (In Russian) v.307, 2004 · 25p
arxiv created 2005/04/20 · arxiv updated 2009/12/01
The new approach to the theory of complex representrations of the finite symmetric groups which based on the notions of Coxeter generators., Gelfand-Zetlin algebras, Hecke algebra, Young-Jucys-Murphi generators and which hardly used inductive structure - is systematically developed. The appearence of Young diagrams, tables is naturally explained - the set of content vectors of all Young tables is the spectra of Gel'fand-Zetlin algebra. The first steps of the theory (the list of the irrediucible representatinos, branching rule, Young orthopgonal form, Murnagan-Nakayama rule etc.)are established.This appraoch canbe used for other classical series, wreath products with symmetric groups. This paper is the revcised version of the paper of the same authors which was published in Selecta MAth. (New Series) V.2(1996).