Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9911334

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

Z. Maassarani

Published Nov 22, 1999• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.cond-mat/9911334

Related papers

New representations of the Hecke algebra and algebraic Bethe Ansatz for an integrable generalized spin ladder

Huan-Qiang Zhou, Holger Frahm, M. D. Gould

This paper has been withdrawn by the authors, due an error in Bethe Ansatz equations (16).

arXiv:cond-mat/9911072•Nov 5, 1999•1 citation

TEMPERLEY-LIEB OPERATORS AND CRITICAL A-D-E MODELS

Paul A. Pearce

A review is given of recent work connecting exactly solvable lattice models with Temperley-Lieb and Hecke algebras, Dynkin diagrams of simply-laced Lie algebras, conformal and modular invariance and Virasoro characters.

International Journal of Modern Physics B•Apr 1, 1990•13 citations

Models solvable by Bethe Ansatz 1

P. P. Kulish

Diagonalization of integrable spin chain Hamiltonians by the quantum inverse scattering method gives rise to the connection with representation theory of different (quantum) algebras. Extending the Schur-Weyl duality between sl2 and the symmetric group SN from the case of the isotropic spin 1/2 chain (XXX-model) to a general spin chains related to the Temperley-Lieb algebra TLN(q) one finds a new quantum algebra Uq(n) with the representation ring equivalent to the sl2 one.

Journal of Generalized Lie Theory and Applications•Jan 1, 2008•3 citations

Multiplicity {A_m} models

Z. Maassarani

Models generalizing the su(2) XX spin-chain were recently introduced. These XXC models also have an underlying su(2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the Am Lie algebras. Integrability of the new models is shown in the context of the quantum inverse scattering method. Their R-matrix is found and shown to yield a representation of the Hecke algebra. The diagonalization of the transfer matrices is carried out using the algebraic Bethe Ansatz. I comment on eventual generalizations and possible links to reaction-diffusion processes.

The European Physical Journal B•Jan 1, 1999•0 citations

Multiplicity A_m Models

Z. Maassarani

Models generalizing the su(2) XX spin-chain were recently introduced. These XXC models also have an underlying su(2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the A_m Lie algebras. Integrability of the new models is shown in the context of the quantum inverse scattering method. Their R-matrix is found and shown to yield a representation of the Hecke algebra. The diagonalization of the transfer matrices is carried out using the algebraic Bethe Ansatz. I comment on eventual generalizations and possible links to reaction-diffusion processes.

arXiv:solv-int/9805009•May 19, 1998•3 citations

A new integral representation for the scalar products of Bethe states for the XXX spin chain

Yoichi Kazama, Shota Komatsu, Takuya Nishimura

arXiv:1304.5011•Journal of High Energy Physics•Sep 1, 2013•33 citations
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.
Models generalizing the su(2) XX spin-chain were recently introduced. These XXC models also have an underlying su(2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the Am Lie algebras. Integrability of the new models is shown in the context of the quantum inverse scattering method. Their R-matrix is found and shown to yield a representation of the Hecke algebra. The diagonalization of the transfer matrices is carried out using the algebraic Bethe Ansatz. I comment on eventual generalizations and possible links to reaction-diffusion processes.
Models generalizing the su(2) XX spin-chain were recently introduced. These XXC models also have an underlying su(2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the A_m Lie algebras. Integrability of the new models is shown in the context of the quantum inverse scattering method. Their R-matrix is found and shown to yield a representation of the Hecke algebra. The diagonalization of the transfer matrices is carried out using the algebraic Bethe Ansatz. I comment on eventual generalizations and possible links to reaction-diffusion processes.