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Loop symmetry of integrable vertex models at roots of unity

Christian Korff, Barry M. McCoy

arXiv:hep-th/0104120Nuclear Physics BDec 1, 200116 citations

The sl2 Loop Algebra Symmetry of the Six-Vertex Model at Roots of Unity

Tetsuo Deguchi, K. Fabricius, Barry M. McCoy

arXiv:cond-mat/9912141Journal of Statistical PhysicsFeb 1, 2001135 citations

MathPhys odyssey 2001 : integrable models and beyond : in honor of Barry M. McCoy

Masaki Kashiwara, 哲二三輪, Barry M. McCoy

Preface * Wavevector-Dependent Susceptibilities in Aperiodic Planar Models * Correlation Functions and Susceptibility in the Z-Invariant Ising Model * A Rapidity-independent Parameter in the Star-Triangle Relation * Evaluation of Integrals Representing Correlations in XXX Heisenberg Spin Chain * A Note on Quotients of the Onsager Algebra * Evaluation Parameters and Bethe Roots for the Six Vertex Model at Roots of Unity * Normalization Factors, Reflection Amplitudes and Integrable Systems * Vertex Operator Algebra Arising from the Minimal Series M(3,p) and Monomial Basis * Paths Crystals and Fermionic Formulae * The Nonlinear Steepest Descent Approach to the Asymtpotis of the Second Painleve Transcendent in the Complex Domain * Generalized Umemura Polynomials and Hirota-Miwa Equation * Correlation Functions of Quantum Integrable Models: The XXZ Spin Chain * On Form Factors of SU(2) Invariant Thirring Model * Integrable Boundaries and Universal TBA Functional Equations * Conformal Field Theories, Graphs and Quantum Algebras * q-Supernomial Coefficients: From Rigging to Ribbons * Separation of Variables for Quantum Integrable Models Related to Uq(slN) * On a Distribution Function Arising in Computational BiologyPreface * Wavevector-Dependent Susceptibilities in Aperiodic Planar Models * Correlation Functions and Susceptibility in the Z-Invariant Ising Model * A Rapidity-independent Parameter in the Star-Triangle Relation * Evaluation of Integrals Representing Correlations in XXX Heisenberg Spin Chain * A Note on Quotients of the Onsager Algebra * Evaluation Parameters and Bethe Roots for the Six Vertex Model at Roots of Unity * Normalization Factors, Reflection Amplitudes and Integrable Systems * Vertex Operator Algebra Arising from the Minimal Series M(3,p) and Monomial Basis * Paths Crystals and Fermionic Formulae * The Nonlinear Steepest Descent Approach to the Asymtpotis of the Second Painleve Transcendent in the Complex Domain * Generalized Umemura Polynomials and Hirota-Miwa Equation * Correlation Functions of Quantum Integrable Models: The XXZ Spin Chain * On Form Factors of SU(2) Invariant Thirring Model * Integrable Boundaries and Universal TBA Functional Equations * Conformal Field Theories, Graphs and Quantum Algebras * q-Supernomial Coefficients: From Rigging to Ribbons * Separation of Variables for Quantum Integrable Models Related to Uq(slN) * On a Distribution Function Arising in Computational Biology

Birkhäuser-Verlag eBooksJan 1, 20022 citations

Solution of the SU(N) vertex model with non-diagonal open boundaries

W. Galléas, Marcio Jose Martins

arXiv:nlin/0407027Physics Letters ADec 24, 200450 citations

TheQ-operator for root-of-unity symmetry in the six-vertex model

Shi-shyr Roan

We construct the explicit Q -operator incorporated with the sl 2 -loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the Q -operator, the six-vertex transfer matrix and fusion matrices are derived from the Bethe equation, parallel to the Onsager-algebra-symmetry discussion in the superintegrable N -state chiral Potts model. We show that the whole set of functional equations is valid for the Q -operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the Q -operator in the symmetry study of root-of-unity six-vertex model from the functional-relation aspect.We construct the explicit Q -operator incorporated with the sl 2 -loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the Q -operator, the six-vertex transfer matrix and fusion matrices are derived from the Bethe equation, parallel to the Onsager-algebra-symmetry discussion in the superintegrable N -state chiral Potts model. We show that the whole set of functional equations is valid for the Q -operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the Q -operator in the symmetry study of root-of-unity six-vertex model from the functional-relation aspect.

arXiv:cond-mat/0602375Journal of Physics A Mathematical and GeneralSep 19, 200614 citations

On the two-point correlation functions for the Uq[SU(2)] invariant spin one-half Heisenberg chain at roots of unity

Haye Hinrichsen B, Paul Martin, V. Rittenberg +1 more

arXiv:hep-th/9310119Nuclear Physics BMar 1, 199416 citations

The spectrum of an open vertex model based on the Uq[SU(2)] algebra at roots of unity

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The spectrum of an open vertex model based on the Uq[SU(2)] algebra at roots of unity

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