Strong Gelfand subgroups of F ≀ Sn

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 [Formula: see text], the wreath product [Formula: see text], where [Formula: see text] is a Young subgroup, is multiplicity-free if and only if [Formula: see text] 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.