Standard modules, radicals, and the valenced Temperley-Lieb algebra

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.