Comments on "New representations of the Hecke algebra and algebraic Bethe Ansatz for an integrable generalized spin ladder", by H.-Q. Zhou, H. Frahm and M.D. Gould, cond-mat/9911072

TL;DR

This paper clarifies that the so-called new Hecke algebra representations are actually known XXC models related to the Temperley-Lieb algebra, correcting previous claims of novelty and discussing related issues.

Contribution

It demonstrates that the claimed new representations are previously known models, specifically the XXC models, and clarifies their algebraic structure as Temperley-Lieb algebra representations.

Findings

The so-called new representations are actually known XXC models.

These models are representations of the Temperley-Lieb algebra.

The paper points out errors and clarifies the algebraic structure involved.

Abstract

The authors of cond-mat/9911072 claim to introduce "new representations of the Hecke algebra." These representations are shown to be the XXC models introduced two years ago in solv-int/9712008, and repeatedly studied and referred to in subsequent papers. They are in fact representations of the Temperley-Lieb algebra. Several other remarks are made and mistakes are pointed out.