A new approach to the representation theory of the symmetric groups, III: Induced representations and the Frobenius--Young correspondence

Details A new approach to the representation theory of the symmetric groups, III: Induced representations and the Frobenius--Young correspondence A new approach to the representation theory of the symmetric groups, III: Induced representations and the Frobenius--Young correspondence

2006-09-09

arxiv.org/abs/math/0609258v1

Mathematics

Representation Theory

22p. Ref.17

Scientific paper

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 \cite{OV, VO}, 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.

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