  We show that the quantum Heisenberg group $H_{q}(1)$ can be obtained by means
of contraction from quantum $SU_q(2)$ group. Its dual Hopf algebra is the
quantum Heisenberg algebra $U_{q}(h(1))$. We derive left and right regular
representations for $U_{q}(h(1))$ as acting on its dual $H_{q}(1)$. Imposing
conditions on the right representation the left representation is reduced to an
irreducible holomorphic representation with an associated quantum coherent
state. By duality, left and right regular representations for quantum
Heisenberg group with the quantum Heisenberg algebra as representation module
are also constructed. As before reduction of left representations leads to
finite dimensional irreducible ones for which the intertwinning operator is
also investigated.
