Abstract
In this work the introduction of generalized A,B,C,D interaction-round-a-face model invariants related to composite braid group representations will be proposed. The invariant polynomials are obtained in the framework of Witten's Chern-Simons theory summarizing recent works on link invariants. The primary intention is to present explicitly neglected results in the latter area and to outline in a pedagogical way the computation of a variety of known and new invariants. The close relationship of the topological interpretation of link invariants and the notion of generalized knot polynomials derived from integrable models in statistical mechanics is emphasized.
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