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Wreath products by the symmetric groups and product posets of Young’s lattices. (English) Zbl 0707.05062
The Young lattice is the poset of all partitions of the set of positive integers, namely almost everywhere null never increasing sequences of non-negative integers with positive sum. Studying the connections between wreath products \(G\wr S_ n\) of a finite group G with a symmetric groups \(S_ n\) and powers of the Young lattice, the author is able to give a complete set of mututally orthogonal eigenvectors for the linear mapping \(Ind^ n_{n-1}\circ Res^ n_{n-1}\) of the vector space of class functions of \(G\wr S_ n\), where \(Ind^ n_{n-1}\) is the induction mapping from (the vector space of class functions of) \(G\wr S_{n-1}\) to \(G\wr S_ n\) and \(Res^ n_{n-1}\) is the restriction mapping from (the vector space of class functions of) \(G\wr S_ n\) to \(G\wr S_{n-1}\).
Reviewer: A.Pasini

MSC:
05E25 Group actions on posets, etc. (MSC2000)
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
06A07 Combinatorics of partially ordered sets
20C30 Representations of finite symmetric groups
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References:
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