  This article concerns a generalization of the Temperley-Lieb algebra,
important in applications to conformal field theory. We call this algebra the
valenced Temperley-Lieb algebra. We prove salient facts concerning this algebra
and its representation theory, which are both of independent interest and used
in our subsequent work, where we uniquely and explicitly characterize the
monodromy invariant correlation functions of certain conformal field theories.
