  Chiral conformal blocks in a rational conformal field theory are a far going
extension of Gauss hypergeometric functions. The associated monodromy
representations of Artin's braid group capture the essence of the modern view
on the subject, which originates in ideas of Riemann and Schwarz. Physically,
such monodromy representations correspond to a new type of braid group
statistics, which may manifest itself in two-dimensional critical phenomena,
e.g. in some exotic quantum Hall states. The associated primary fields satisfy
R-matrix exchange relations. The description of the internal symmetry of such
fields requires an extension of the concept of a group, thus giving room to
quantum groups and their generalizations. We review the appearance of braid
group representations in the space of solutions of the Knizhnik - Zamolodchikov
equation, with an emphasis on the role of a regular basis of solutions which
allows us to treat the case of indecomposable representations as well.
