Brauer loops and the commuting variety

DOI10.1088/1742-5468/2005/01/P01006zbMath1072.82585arXivmath/0410392WikidataQ60692396 ScholiaQ60692396MaRDI QIDQ3160141

Bernard Nienhuis, Jan De Gier

Publication date: 1 February 2005

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

Full work available at URL: https://arxiv.org/abs/math/0410392

zbMATH Keywords

solvable lattice modelsintegrable spin chains (vertex models)algebraic structures of integrable modelsloop models and polymers

Mathematics Subject Classification ID

Exactly solvable models; Bethe ansatz (82B23) Operator algebra methods applied to problems in quantum theory (81R15) Associative rings and algebras arising under various constructions (16S99)

Related Items (8)

Notes on Schubert, Grothendieck and key polynomials ⋮ Type \(\widehat{\mathrm C}\) Brauer loop schemes and loop model with boundaries ⋮ Inhomogeneous model of crossing loops and multidegrees of some algebraic varieties ⋮ A scheme related to the Brauer loop model ⋮ The Brauer loop scheme and orbital varieties ⋮ The dilute Temperley–Lieb O(n  =  1) loop model on a semi infinite strip: the sum rule ⋮ On two-point boundary correlations in the six-vertex model with domain wall boundary conditions ⋮ Monte Carlo study of the hull distribution for theq= 1 Brauer model

Uses Software

• Macaulay2
• OEIS

Cites Work

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• On an algebraic approach to higher dimensional statistical mechanics
• 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
• Dense Loops, Supersymmetry, and Goldstone Phases in Two Dimensions
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• Temperley Lieb stochastic processes
• Intersecting Loop Model as a Solvable Super Spin Chain
• Spin chains and combinatorics

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