  We derive two-sided bounds for the Newton and Poisson kernels of the
$W$-invariant Dunkl Laplacian in geometric complex case when the multiplicity
$k(\alpha)=1$, i.e. for flat complex symmetric spaces. For the invariant
Dunkl-Poisson kernel $P^W(x,y)$, the estimates are $$ P^W(x,y)\asymp
\frac{P^{{\bf R}^d}(x,y)}{\prod_{\alpha > 0 \ }|x-\sigma_\alpha
y|^{2k(\alpha)}},$$ where the $\alpha$'s are the positive roots of a root
system acting in ${\bf R}^d$, the $\sigma_\alpha$'s are the corresponding
symmetries and $P^{{\bf R}^d}$ is the classical Poisson kernel in ${{\bf
R}^d}$. Analogous bounds are proven for the Newton kernel when $d\ge 3$. The
same estimates are derived in the rank one direct product case $\mathbb Z_2^N$
and conjectured for general $W$-invariant Dunkl processes. As an application,
we get a two-sided bound for the Poisson and Newton kernels of the classical
Dyson Brownian motion and of the Brownian motions in any Weyl chamber.
