  A representation of the group element (also known as ``universal ${\cal
T}$-matrix'') which satisfies $\Delta(g) = g\otimes g$, is given in the form $$
g = \left(\prod_{s=1}^{d_B}\phantom.^>\ {\cal
E}_{1/q_{i(s)}}(\chi^{(s)}T_{-i(s)})\right) q^{2\vec\phi\vec H}
\left(\prod_{s=1}^{d_B}\phantom.^<\ {\cal E}_{q_{i(s)}}(\psi^{(s)}
T_{+i(s)})\right)$$ where $d_B = \frac{1}{2}(d_G - r_G)$, $q_i = q^{||
\vec\alpha_i||^2/2}$ and $H_i = 2\vec H\vec\alpha_i/||\vec\alpha_i||^2$ and
$T_{\pm i}$ are the generators of quantum group associated respectively with
Cartan algebra and the {\it simple} roots. The ``free fields'' $\chi,\
\vec\phi,\ \psi$ form a Heisenberg-like algebra: $\psi^{(s)}\psi^{(s')} =
q^{-\vec\alpha_{i(s)} \vec\alpha_{i(s')}} \psi^{(s')}\psi^{(s)}, &
\chi^{(s)}\chi^{(s')} = q^{-\vec\alpha_{i(s)}\vec\alpha_{i(s')}}
\chi^{(s')}\chi^{(s)}& {\rm for} \ s<s', \\ q^{\vec h\vec\phi}\psi^{(s)} =
q^{\vec h\vec\alpha_{i(s)}} \psi^{(s)}q^{\vec h\vec\phi}, & q^{\vec
h\vec\phi}\chi^{(s)} = q^{\vec h \vec\alpha_{i(s)}}\chi^{(s)}q^{\vec
h\vec\phi}, & \\ &\psi^{(s)} \chi^{(s')} = \chi^{(s')}\psi^{(s)} & {\rm for\
any}\ s,s'.$ We argue that the $d_G$-parametric ``manifold'' which $g$ spans in
the operator-valued universal envelopping algebra, can also be invariant under
the group multiplication $g \rightarrow g'\cdot g''$. The universal ${\cal
R}$-matrix with the property that ${\cal R} (g\otimes I)(I\otimes g) =
(I\otimes g)(g\otimes I){\cal R}$ is given by the usual formula $${\cal R} =
q^{-\sum_{ij}^{r_G}||\vec\alpha_i||^2|| \vec\alpha_j||^2
(\vec\alpha\vec\alpha)^{-1}_{ij}H_i \otimes H_j}\prod_{ \vec\alpha >
0}^{d_B}{\cal E}_{q_{\vec\alpha}}\left(-(q_{\vec\alpha}-
q_{\vec\alpha}^{-1})T_{\vec\alpha}\otimes T_{-\vec\alpha}\right).$$
