  The appearance of quantum groups in conformal field theories is traced back
to the Poisson-Lie symmetries of the classical chiral theory. A geometric
quantization of the classical theory deforms the Poisson-Lie symmetries to the
quantum group ones. This elucidates the fundamental role of chiral symmetries
that quantum groups play in conformal models. As a byproduct, one obtains a
more geometric approach to the representation theory of quantum groups.
