Automorphisms and generalized involution models of finite complex reflection groups

We prove that a finite complex reflection group has a generalized involution model, as defined by Bump and Ginzburg, if and only if each of its irreducible factors is either G(r,p,n) with gcd(p,n)=1; G(r,p,2) with r/p odd; or G23, the Coxeter group of type H3. We additionally provide explicit formulas for all automorphisms of G(r,p,n), and construct new Gelfand models for the groups G(r,p,n) with gcd(p,n)=1.