Quantum Knizhnik–Zamolodchikov equation: reflecting boundary conditions and combinatorics

DOI10.1088/1742-5468/2007/12/P12009zbMath1456.82116arXiv0709.3410OpenAlexW2118452336MaRDI QIDQ5239339

Paul Zinn-Justin, Philippe Di Francesco

Publication date: 22 October 2019

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.3410

zbMATH Keywords

solvable lattice modelsalgebraic structures of integrable modelsloop models and polymers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Statistical mechanics of polymers (82D60) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (19)

On some polynomials enumerating Fully Packed Loop configurations: evaluation at negative values ⋮ Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder: II. Rotated lattice ⋮ Correlation functions of the half-infinite XXZ spin chain with a triangular boundary ⋮ Deformed Kazhdan-Lusztig elements and Macdonald polynomials ⋮ On the weighted enumeration of alternating sign matrices and descending plane partitions ⋮ On some ground state components of the O(1) loop model ⋮ The exact finite size ground state of the O(n= 1) loop model with open boundaries ⋮ Correlation functions and the boundary qKZ equation in a fractured XXZ chain ⋮ Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors ⋮ On some polynomials enumerating fully packed loop configurations ⋮ Boundary quantum Knizhnik-Zamolodchikov equations and fusion ⋮ Punctured plane partitions and the \(q\)-deformed Knizhnik-Zamolodchikov and Hirota equations ⋮ An operator formula for the number of halved monotone triangles with prescribed bottom row ⋮ Fully Packed Loop Models on Finite Geometries ⋮ Towers of solutions of qKZ equations and their applications to loop models ⋮ The open XXZ chain at Δ = −1/2 and the boundary quantum Knizhnik–Zamolodchikov equations ⋮ Koornwinder polynomials and the \(XXZ\) spin chain ⋮ Connection problems for quantum affine KZ equations and integrable lattice models ⋮ Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder

Cites Work

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• Inhomogeneous model of crossing loops and multidegrees of some algebraic varieties
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• Alternating sign matrices and descending plane partitions
• Quantum affine algebras and holonomic difference equations
• Meanders and the Temperley-Lieb algebra
• Difference equations in spin chains with a boundary
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• Loops, matchings and alternating-sign matrices
• A scheme related to the Brauer loop model
• Combinatorial nature of the ground-state vector of the \(\mathrm{O}(1)\) loop model
• The quantum symmetricXXZchain at Δ = -½, alternating-sign matrices and plane partitions
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• A general formula for soliton form factors in the quantum sine-Gordon model
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• Inhomogeneous loop models with open boundaries
• The quantum Knizhnik–Zamolodchikov equation, generalized Razumov–Stroganov sum rules and extended Joseph polynomials

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