KNOT INVARIANTS ASSOCIATED WITH A PARTICULAR N-]INFINITY CONTINUOUS LIMIT OF THE BAXTER-BAZHANOV MODEL

First we briefly recall the definition of the three-dimensional Baxter -Bazhanov lattice model. The spins of this model are elements of Z(N) and the R-matrix is associated to the algebra U(q)sl(n) if q is a prim itive Nth root of unity. Then we construct a particular N --> infinity limit of the model, in which it is meaningful to interpret the spins as elements of R and which gives the free Gaussian boson model. Finall y, we study special limits of the rapidity variables in which we obtai n braid group representations and we show that for n odd the associate d knot invariants are given by the inverse of products of Alexander po lynomials, evaluated at certain roots of unity.