  A simple connection between the universal $R$ matrix of $U_q(sl(2))$ (for
spins $\demi$ and $J$) and the required form of the co-product action of the
Hilbert space generators of the quantum group symmetry is put forward. This
gives an explicit operator realization of the co-product action on the
covariant operators. It allows us to derive the quantum group covariance of the
fusion and braiding matrices, although it is of a new type: the generators
depend upon worldsheet variables, and obey a new central extension of
$U_q(sl(2))$ realized by (what we call) fixed point commutation relations. This
is explained by showing that the link between the algebra of field
transformations and that of the co-product generators is much weaker than
previously thought. The central charges of our extended $U_q(sl(2))$ algebra,
which includes the Liouville zero-mode momentum in a nontrivial way are related
to Virasoro-descendants of unity. We also show how our approach can be used to
derive the Hopf algebra structure of the extended quantum-group symmetry
$U_q(sl(2))\odot U_{\qhat}(sl(2))$ related to the presence of both of the
screening charges of 2D gravity.
