  A quantum group covariant extension of the chiral parts of the
Wess-Zumino-Novikov-Witten model on a compact Lie group G gives rise to two
matrix algebras with non-commutative entries. These are generated by "chiral
zero modes" which combine in the 2D model into "Q-operators" which encode
information about the internal symmetry and the fusion ring. We review earlier
results about the SU(n) WZNW Q-algebra and its Fock representation for n=2 and
display the first steps towards their generalization to higher n.
