  In this paper, we shall establish the Mackey formulas in the following two
set ups: (i) on the tensor induction and restriction functors on the modules
over cyclotomic Hecke algebras (Ariki-Koike algebras) and their standard
subalgebras of parabolic subgroups. (ii) on the Bezrukavnikov-Etingof induction
and restriction functors among categories O of rational Cherednik algebras for
the complex reflection group of type G(r, 1, n) and their parabolic subgroups.
