  This paper is a short account of the construction of a new class of the
infinite-dimensional representations of the quantum groups. The examples
include finite-dimensional quantum groups $U_q(\mathfrak{g})$, Yangian
$Y(\mathfrak{g})$ and affine quantum groups at zero level
  $U_q(\hat{\mathfrak{g}})_{c=0}$ corresponding to an arbitrary
finite-dimensional semisimple Lie algebra $\mathfrak{g}$. At the intermediate
step we construct the embedding of the quantum groups into the algebra of the
rational functions on the quantum multi-dimensional torus. The explicit
parameterization of the quantum groups used in this paper turns out to be
closely related to the parameterization of the moduli spaces of the monopoles.
As a result the proposed constructions of the representations provide a
quantization of the moduli spaces of the monopoles on $\RR^3$ and $\RR^2\times
S^1$.
