Strong Gelfand subgroups of $F\wr S_n$

Abstract

The multiplicity-free subgroups (strong Gelfand subgroups) of wreath products are investigated. Various useful reduction arguments are presented. In particular, we show that for every finite group $F$, the wreath product $F\wr S_{\lambda }$, where $S_{\lambda }$ is a Young subgroup, is multiplicity-free if and only if $\lambda$ is a partition with at most two parts, the second part being 0,1, or 2. Furthermore, we classify all multiplicity-free subgroups of hyperoctahedral groups. Along the way, we derive various decomposition formulas for the induced representations from some special subgroups of hyperoctahedral groups.

Comments are always welcome! v2 fixes some minor mistakes, and corrects Table 1, that had previously missed a couple of strong Gelfand subgroups