  Considering a multi-dimensional $q$-oscillator invariant under the (non
quantum) group $U(n)$, we construct a $q$-deformed Levi-Civita epsilon tensor
from the inner product states. The invariance of this $q$-epsilon tensor is
shown to yield the quantum group $SL_{q}(n)$ and establishes the relationship
of the $U(n)$ invariant $q$-oscillator to quantum groups and quantum group
related oscillators. Furthermore the $q$-epsilon tensor provides the connection
between $SL_{q}(n)$ and the volume element of the quantum hyper plane.
