Yang-Baxter relation, exactly solvable models and link polynomials

Abstract

Presented is a general theory to construct link polynomials, topological invariants for knots and links, from exactly solvable (integrable) models. Representations of the braid group and the Markov traces on the representations are made through the general theory which is based on fundamental properties of exactly solvable models. Various examples including Alexander, Jones, Kauffman and a hierarchy of link polynomials are explicitly shown.KeywordsSolvable ModelBraid GroupJones PolynomialVertex ModelReidemeister MoveThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.