Knot invariants associated with a particularN→∞ continuous limit of the Baxter-Bazhanov model

Abstract

First we briefly recall the definition of the three-dimensional Baxter-Bazhanov lattice model. The spins of this model are elements ofZN and theR-matrix is associated to the algebraUqsl(n) ifq is a primitiveNth root of unity. Then we construct a particularN→∞ limit of the model, in which it is meaningful to interpret the spins as elements ofR and which gives the free Gaussian boson model. Finally, we study special limits of the rapidity variables in which we obtain braid group representations and we show that forn odd the associated knot invariants are given by the inverse of products of Alexander polynomials, evaluated at certain roots of unity.