Even and Odd Q-coherent State Representations of the Q-deformed Heisenberg-Weyl Algebra

We construct explicitly even and odd q-coherent states. These q-coherent states are introduced in terms of the q-functions defined in the paper. It is shown that the even and odd q-coherent states form a kind of representations of the q-deformed Heisenberg-Weyl algebra which is realized in the form of matrix q-differential operators in the even and odd q-coherent state space. We also analyse some different between the even and odd q-CSs and the usual even and odd CSs.