Loop model with mixed boundary conditions,qKZ equation and alternating sign matrices

DOI10.1088/1742-5468/2007/01/P01007zbMath1456.82329arXivmath-ph/0610067OpenAlexW3098863958MaRDI QIDQ5239320

Paul Zinn-Justin

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/math-ph/0610067

zbMATH Keywords

solvable lattice modelsloop models and polymerstopology and combinatorics

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (10)

Exact spin quantum Hall current between boundaries of a lattice strip ⋮ Deformed Kazhdan-Lusztig elements and Macdonald polynomials ⋮ The exact finite size ground state of the O(n= 1) loop model with open boundaries ⋮ Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP ⋮ The dilute Temperley–Lieb O(n  =  1) loop model on a semi infinite strip: the ground state ⋮ The dilute Temperley–Lieb O(n  =  1) loop model on a semi infinite strip: the sum rule ⋮ Fully Packed Loop Models on Finite Geometries ⋮ The Razumov–Stroganov conjecture: stochastic processes, loops and combinatorics ⋮ Boundary transfer matrices and boundary quantum KZ equations ⋮ Koornwinder polynomials and the \(XXZ\) spin chain

Cites Work

• \(O(1)\) loop model with different boundary conditions and symmetry classes of alternating-sign matrices
• Inhomogeneous model of crossing loops and multidegrees of some algebraic varieties
• On baxterized solutions of reflection equation and integrable chain models
• Quantum affine algebras and holonomic difference equations
• The blob algebra and the periodic Temperley-Lieb algebra
• Around the Razumov-Stroganov conjecture: proof of a multi-parameter sum rule
• Symmetry classes of alternating-sign matrices under one roof
• On polynomials interpolating between the stationary state of a \(O (n)\) model and a Q.H.E. ground state
• Quantum incompressibility and Razumov Stroganov type conjectures
• Enumeration of symmetry classes of alternating sign matrices and characters of classical groups
• Loops, matchings and alternating-sign matrices
• 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
• Refined Razumov–Stroganov conjectures for open boundaries
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• Temperley Lieb stochastic processes
• Algebraic structure of translation-invariant spin-1/2xxzandq-Potts quantum chains
• Boundary conditions for integrable quantum systems
• Boundary qKZ equation and generalized Razumov–Stroganov sum rules for open IRF models
• Totally symmetric self-complementary plane partitions and the quantum Knizhnik–Zamolodchikov equation: a conjecture
• Inhomogeneous loop models with open boundaries
• The quantum Knizhnik–Zamolodchikov equation, generalized Razumov–Stroganov sum rules and extended Joseph polynomials

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