  In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24
(2010), 370--393] it is constructed a uniform Gelfand model for all
non-exceptional irreducible complex reflection groups which are involutory.
This model can be naturally decomposed into the direct sum of submodules
indexed by symmetric conjugacy classes, and in this paper we present a simple
combinatorial description of the irreducible decomposition of these submodules
if the group is the wreath product of a cyclic group with a symmetric group.
This is attained by showing that such decomposition is compatible with the
generalized Robinson-Schensted correspondence for these groups.
