Q-OSCILLATORS, THE Q-EPSILON TENSOR AND QUANTUM GROUPS

Considering a multi-dimensional q-oscillator invariant under the (non- quantum) group U(n), we construct a q-deformed Levi-Civita epsilon ten ser from the inner product states. The invariance of this q-epsilon te nser 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 tenser pr ovides the connection between SL(q)(n) and the volume element of the q uantum hyperplane.