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

Nuclear Physics B

Integrable models through representations of the hecke algebra

Nir Sochen

Published Aug 1, 1991• 12 citations
Publisher
DOI
10.1016/0550-3213(91)90418-w

Related papers

Chain models on hecke algebra for corner type representations

A.P. Isaev, O. Ogievetsky, A.F. Os'kin

arXiv:0710.0261•Reports on Mathematical Physics•Apr 1, 2008•7 citations

From affine Hecke algebras to boundary symmetries

Anastasia Doikou

arXiv:math-ph/0409060•Nuclear Physics B•Aug 9, 2005•38 citations

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

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.

arXiv:cond-mat/9911334•Nov 22, 1999•0 citations

Quantum Groups and Integrable Models

Leon A. Takhtajan

Advanced studies in pure mathematics•Jun 17, 2018•32 citations

On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary

Anastasia Doikou, Paul Martin

Motivated by a study of the crossing symmetry of the asymmetric twin or ‘gemini’ representation of the affine Hecke algebra we give a construction for crossing tensor space representations of ordinary Hecke algebras. These representations build solutions to the Yang–Baxter equation satisfying the crossing condition (that is, integrable quantum spin chains). We show that every crossing representation of the Temperley–Lieb algebra appears in this construction, and in particular that this construction builds new representations. We extend these to new representations of the blob algebra, which build new solutions to the boundary Yang–Baxter equation (i.e. open spin chains with integrable boundary conditions). We prove that the open spin chain Hamiltonian derived from Sklyanin’s commuting transfer matrix using such a solution can always be expressed as the representation of an element of the blob algebra, and determine this element. We determine the representation theory (irreducible content) of the new representations and hence show that all such Hamiltonians have the same spectrum up to multiplicity, for any given value of the algebraic boundary parameter. (A corollary is that our models have the same spectrum as the open XXZ chain with nondiagonal boundary—despite differing from this model in having reference states.) Using these multiplicity data, and other ideas, we investigate the underlying quantum group symmetry of the new Hamiltonians. We derive the form of the spectrum and the Bethe ansatz equations.

arXiv:hep-th/0503019•Journal of Statistical Mechanics Theory and Experiment•Jun 8, 2006•30 citations

Aspects of Integrable Models

Costas John Efthimiou

•Jan 1, 1994•0 citations
Motivated by a study of the crossing symmetry of the asymmetric twin or ‘gemini’ representation of the affine Hecke algebra we give a construction for crossing tensor space representations of ordinary Hecke algebras. These representations build solutions to the Yang–Baxter equation satisfying the crossing condition (that is, integrable quantum spin chains). We show that every crossing representation of the Temperley–Lieb algebra appears in this construction, and in particular that this construction builds new representations. We extend these to new representations of the blob algebra, which build new solutions to the boundary Yang–Baxter equation (i.e. open spin chains with integrable boundary conditions). We prove that the open spin chain Hamiltonian derived from Sklyanin’s commuting transfer matrix using such a solution can always be expressed as the representation of an element of the blob algebra, and determine this element. We determine the representation theory (irreducible content) of the new representations and hence show that all such Hamiltonians have the same spectrum up to multiplicity, for any given value of the algebraic boundary parameter. (A corollary is that our models have the same spectrum as the open XXZ chain with nondiagonal boundary—despite differing from this model in having reference states.) Using these multiplicity data, and other ideas, we investigate the underlying quantum group symmetry of the new Hamiltonians. We derive the form of the spectrum and the Bethe ansatz equations.