REPRESENTATIONS OF BRAID-GROUPS AND THE QUANTUM YANG-BAXTER EQUATION

We are going to study the construction of new representations of braid groups and solutions of quantum Yang-Baxter (=QYBE) from existing ones via cabling. This can be applied for the construction of new link invariants from a given one for a wide class of invariants. For the example of the 2-variable generalization of the Jones polynomial, this yields for each Young diagram a 1-parameter family of representations of the braid groups and a 2-variable link invariant. Using the braid representations from the QYBE, one obtains a 1-variable link invariant for each irreducible representation of a classical Lie algebra. © 1990 by Pacific Journal of Mathematics.