THE CHIRAL POTTS-MODEL AND ITS ASSOCIATED LINK INVARIANT

A new link invariant is derived using the exactly solvable chiral Pott s model and a generalized Gaussian summation identity. Starting from a general formulation of link invariants using edge-interaction spin mo dels, we establish the uniqueness of the invariant for self-dual model s. We next apply the formulation to the self-dual chiral Potts model, and obtain a link invariant in the form of a lattice sum defined by a matrix associated with the link diagram. A generalized Gaussian summat ion identity is then used to carry out this lattice sum, enabling us t o cast the invariant into a tractable form. The resulting expression f or the link invariant is characterized by roots of unity and does not appear to belong to the usual quantum group family of invariants. A ta ble of invariants for links with up to eight crossings is given.