  In this paper we construct a large class of multiplication operators on
reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to
the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms
of the unit disc $\mathbb D$. For every $m \in \N$ we have a family of
operators depending on $m+1$ positive real parameters. The kernel function is
calculated explicitly. It is proved that each of these operators is bounded,
lies in the Cowen-Douglas class of $\mathbb D$ and is irreducible. These
operators are shown to be mutually pairwise unitarily inequivalent.
