  Gaussian quasi-invariant measures on groups of diffeomorphisms and loop
groups G relative to dense subgroups G' were constructed. In the
non-Archimedean case the wider class of measures was investigated, than in the
real case. The cases of Riemann and non-Archimedean manifolds were considered.
This article is related with unitary representations of G' associated with
Poisson measures on $G^{\bf N}$ and uses quasi-invariant measures on G from the
previous works. Several groups are considered: (1) (a) diffeomorphisms and (b)
loop groups of real manifolds, (2) (a) diffeomorphisms and (b) loop groups of
non-Archimedean manifolds over local fields. Besides these four cases further
the fifth and the sixth cases are considered: for (3) (a) real and (b)
non-Archimedean groups of diffeomorphisms Diff(M) representations associated
with Poisson measures on configuration spaces $\Gamma_M$ contained in products
of manifolds $M^{\bf N}$ are investigated. Here the cases of
infinite-dimensional Banach manifold M (3) (a), non-Archimdean locally compact
and non-locally compact Banach manifolds (3) (b) are investigated.
