  We study the intermediate liberation problem for the real and complex unitary
and reflection groups, namely $O_N,U_N,H_N,K_N$. For any of these groups $G_N$,
the problem is that of understanding the structure of the intermediate quantum
groups $G_N\subset G_N^\times\subset G_N^+$, in terms of the recently
introduced notions of "soft" and "hard" liberation. We solve here some of these
questions, our key ingredient being the generation formula
$H_N^{[\infty]}=<H_N,T_N^+>$, coming via crossed product methods. Also, we
conjecture the existence of a "contravariant duality" between the liberations
of $H_N$ and of $U_N$, as a solution to the lack of a covariant duality between
these liberations.
