The Early History of the Integrable Chiral Potts Model and the Odd-Even Problem

TL;DR

This paper reviews the historical discovery of the integrable chiral Potts model, explores its potential higher-genus generalizations, and discusses quantum group aspects related to odd-even $N$ issues and coproducts.

Contribution

It provides a historical overview and insights into higher-genus models and quantum group structures, especially addressing odd-even $N$ distinctions and coproduct applications.

Findings

Historical account of the model's discovery

Potential for discovering higher-genus models

Quantum group analysis related to odd-even $N$

Abstract

In the first part of this paper I shall discuss the round-about way of how the integrable chiral Potts model was discovered about 30 years ago. As there should be more higher-genus models to be discovered, this might be of interest. In the second part I shall discuss some quantum group aspects, especially issues of odd versus even $N$ related to the Serre relations conjecture in our quantum loop subalgebra paper of 5 years ago and how we can make good use of coproducts, also borrowing ideas of Drinfeld, Jimbo, Deguchi, Fabricius, McCoy and Nishino.