Involutory reflection groups and their models
A finite subgroup of GL(n, C) is involutory if the sum of the
dimensions of its irreducible complex representations is given by the number of
absolute involutions in the group. A uniform combinatorial model is constructed
for all non-exceptional irreducible complex reflection groups which are
involutory including, in particular, all infinite families of finite
irreducible Coxeter groups.
We introduce the class of projective reflection groups which includes all
complex reflection groups. We show that several aspects involving the
combinatorics and the representation theory of all non exceptional irreducible
complex reflection groups find a natural description in this wider setting.