Combinatorial point for higher spin loop models

Abstract

Integrable loop models associated with higher representations (spin k/2) of U_q(sl(2)) are investigated at the point q=-e^{iπ/(k+2)}. The ground state eigenvalue and eigenvectors are described. Introducing inhomogeneities into the models allows to derive a sum rule for the ground state entries.

arXiv commentlatest version adds some references

References in corpus (9)

• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Meanders and the Temperley-Lieb algebra
• Combinatorial nature of ground state vector of O(1) loop model
• Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
• Inhomogeneous loop models with open boundaries
• Boundary qKZ equation and generalized Razumov-Stroganov sum rules for open IRF models
• Higher spin vertex models with domain wall boundary conditions
• Enumeration of Symmetry Classes of Alternating Sign Matrices and Characters of Classical Groups
• A scheme related to the Brauer loop model

Cited by in corpus (16)

• Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
• The eight-vertex model and lattice supersymmetry
• Logarithmic Superconformal Minimal Models
• Fusion hierarchies, T-systems and Y-systems of logarithmic minimal models
• Finite size emptiness formation probability of the XXZ spin chain at $\Delta =-1/2$
• Factorised solutions of Temperley-Lieb $q$KZ equations on a segment
• Multi-state asymmetric simple exclusion processes
• Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry
• Critical behaviour of loop models on causal triangulations
• Doubly-refined enumeration of Alternating Sign Matrices and determinants of 2-staircase Schur functions
• Symmetry classes of alternating sign matrices in the nineteen-vertex model
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point
• Higher spin polynomial solutions of quantum Knizhnik--Zamolodchikov equation
• Integrability of planar-algebraic models
• Integrable models from singly generated planar algebras
• Higher Spin Alternating Sign Matrices