Braid group representations arising from the generalized chiral Potts models

Etsurō Date, Michio Jimbo, Kei Miki and Tetsuji Miwa

Vol. 154 (1992), No. 1, 37–66

DOI: 10.2140/pjm.1992.154.37

Abstract

A class of braid group representations are constructed for each non-singular bilinear form B : (Z∕NZ)^l × (Z∕NZ)^l → Z∕NZ with N odd. Associated link invariants are given as a Gauss sum involving the Seifert matrix and B. With a special choice of B these representations are Yang-Baxterized to the sl(n) generalizations of the chiral Potts model discovered recently.

Mathematical Subject Classification 2000

Primary: 20F36

Secondary: 57M25, 82B23

Milestones

Received: 13 December 1990

Published: 1 May 1992