A Positive integral property on the ground state of the two-boundary Temperley--Lieb Hamiltonian

2014/12/24 by Keiichi Shigechi, Shigechi, Keiichi · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP #math.QA #nlin.SI

paper · pdf · doi:10.48550/arxiv.1412.7617

62 pages

arxiv created 2014/12/24 · openalex publication_date 2014/12/24 · arxiv updated 2014/12/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the two-boundary Temperley--Lieb O(n) loop model on Kazhdan--Lusztig bases of type A and B. We obtain explicit expressions of the ground state of the two-boundary Temperley--Lieb Hamiltonian by means of a coideal subalgebra of U_q(\mathfraksl₂). This ground state possesses a positive integral property. We conjecture that some components of the ground state are directly related to an enumeration of binary or permutation matrices.

Citations

• Kazhdan-Lusztig polynomials for the Hermitian symmetric pair (B_N,A_N-1)
• Quantum Symmetric Pairs and Their Zonal Spherical Functions

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• Symmetric Dyck tilings, ballot tableaux and tree-like tableaux of shifted shapes

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