Representations of braid groups and the quantum Yang-Baxter equation

Hans Wenzl

Vol. 145 (1990), No. 1, 153–180

DOI: 10.2140/pjm.1990.145.153

Abstract

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.

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 20F36, 82B23

Milestones

Received: 15 November 1988

Published: 1 September 1990