Knots, Links, Braids and Exactly Solvable Models in Statistical Mechanics

Aug 28, 1987
48 pages
Published in:
  • Commun.Math.Phys. 117 (1988) 243
Report number:
  • Print-87-0692 (TOKYO U.,KOMABA)

Citations per year

1988199720062015202402468101214
Abstract: (Springer)
We present a general method to construct the sequence of new link polynomials and its two variable extension from exactly solvable models in statistical mechanics. First, we find representations of the braid group from the Boltzmann weights of the exactly solvable models. Second, we give the Markov traces associated with new braid group representations and using them construct new link polynomials. Third, we extend the theory into a two-variable version of the new link polynomials. Throughout the paper, we emphasize the essential roles played by the exactly solvable models and the underlying Yang-Baxter relation.
  • statistical mechanics
  • integrability
  • knot theory: Jones polynomial
  • braid group
  • Yang-Baxter equation
  • bibliography