Gelfand models and Robinson-Schensted correspondence

In F. Caselli (Involutory reflection groups and their models, J. Algebra 24:370–393, 2010), a uniform Gelfand model is constructed for all nonexceptional irreducible complex reflection groups which are involutory. Such models can be naturally decomposed into the direct sum of submodules indexed by Sn-conjugacy classes, and we present here a general result that relates the irreducible decomposition of these submodules with the projective Robinson–Schensted correspondence. This description also reflects, in a very explicit way, the existence of split representations for these groups.