Wreath products by the symmetric groups and product posets of Young's lattices

Abstract

In this note we study the connections between the wreath products Γ≀ G n of a finite group Γ by the symmetric groups G n and the product poset Y r of Young's lattices Y. We construct a generalized Robinson-Schensted correspondence for Γ≀ G n . And we give a complete set of orthogonal eigenvectors for the linear transformation Γ≀G n Γ≀G n−t of the vector space of class functions on Γ≀G n Γ≀G n−1 .