A new approach to the representation theory of the symmetric groups. III. Induced representations and the Frobenius–Young correspondence

We give a new (inductive) proof of the classical Frobenius–Young correspondence between irreducible complex representations of the symmetric group and Young diagrams, using the new approach, suggested in paper by A. Okounkov and the author, to determining this correspondence. We also give linear relations between Kostka numbers that follow from the decomposition of the restrictions of induced representations to the previous symmetric subgroup. We consider a realization of representations induced from Young subgroups in polylinear forms and describe its relation to Specht modules.