Bimodule structure in the periodic \({\mathfrak g}\ell (1|1)\) spin chain

DOI10.1016/j.nuclphysb.2013.02.017zbMath1262.81159arXiv1112.3407OpenAlexW1673812652MaRDI QIDQ1950591

Azat M. Gainutdinov, N. Read, Hubert Saleur

Publication date: 13 May 2013

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.3407

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Supersymmetric field theories in quantum mechanics (81T60) Continuum limits in quantum field theory (81T27) Applications of selfadjoint operator algebras to physics (46L60) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (13)

A fusion for the periodic Temperley-Lieb algebra and its continuum limit ⋮ The periodic \(s(2|1)\) alternating spin chain and its continuum limit as a bulk logarithmic conformal field theory at \(c = 0\) ⋮ On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories ⋮ Spin chains as modules over the affine Temperley-Lieb algebra ⋮ Associative algebraic approach to logarithmic CFT in the bulk: the continuum limit of the \(\mathfrak{gl}(1|1)\) periodic spin chain, Howe duality and the interchiral algebra ⋮ Continuum limit and symmetries of the periodic \({\mathfrak g}\ell (1|1)\) spin chain ⋮ A physical approach to the classification of indecomposable Virasoro representations from the blob algebra ⋮ Modular invariant partition function of critical dense polymers ⋮ Operator content of the critical Potts model in \(d\) dimensions and logarithmic correlations ⋮ On the reality of spectra ofU_q(sl₂)-invariant XXZ Hamiltonians ⋮ The action of the Virasoro algebra in quantum spin chains. I: The non-rational case ⋮ of anyonic chains ⋮ Boundary algebras and Kac modules for logarithmic minimal models

Cites Work

• Associative algebraic approach to logarithmic CFT in the bulk: the continuum limit of the \(\mathfrak{gl}(1|1)\) periodic spin chain, Howe duality and the interchiral algebra
• Lusztig limit of quantum \(s\ell (2)\) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
• On an algebraic approach to higher dimensional statistical mechanics
• The blob algebra and the periodic Temperley-Lieb algebra
• The representation theory of affine Temperley-Lieb algebras
• A quotient of the affine Hecke algebra in the Brauer algebra
• Cellular algebras
• Continuum limit and symmetries of the periodic \({\mathfrak g}\ell (1|1)\) spin chain
• Enlarged symmetry algebras of spin chains, loop models, and \(S\)-matrices
• Associative-algebraic approach to logarithmic conformal field theories
• A physical approach to the classification of indecomposable Virasoro representations from the blob algebra
• On the Affine Temperley-Lieb Algebras
• The \(sl_2\) loop algebra symmetry of the six-vertex model at roots of unity
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