  Let $\Gamma_{F,n}$ be the Hermitian modular group of degree $n>1$ in sense of
Hel Braun with respect to an imaginary quadratic field $F$. Let $r$ be a
natural number. There exists a multiplier system of weight $1/r$ (equivalently
a Hermitian modular form of weight $k+1/r$, $k$ integral) on some congruence
group if and only if $r=1$ or $2$. This follows from a much more general
construction of Deligne [De] combining it with results of Hill [Hi], Prasad [P]
and Prasad-Rapinchuk [PR]. As far as we know, the systems of weight $1/2$ have
not yet been described explicitly. Remarkably Haowu Wang [Wa] gave an example
of a modular form of half integral weight. Actually he constructs a Borcherds
product of weight $23/2$ for a group of type $O(2,4)$. This group is isogenous
to the group $U(2,2)$ that contains the Hermitian modular groups of degree two.
In this paper we want to study such multiplier systems. If one restricts them
to the unimodular group one obtains a usual character. Our main result states
that the kernel of this character is a non-congruence subgroup. For
sufficiently small $\Gamma$ it coincides with the group described by Kubota in
the case $n=2$ and by Bass Milnor Serre in the case $n>2$.
