qKZ equations and ground state of the O(1) loop model with open boundary conditions

2009/03/30 by Luigi Cantini, Cantini, Luigi
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Chromodynamics and Particle Interactions #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.0903.5050

29 pages; 20 figures

arxiv created 2009/03/30 · openalex publication_date 2009/03/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the qKZ equations based on the two boundaries Temperley Lieb algebra. We construct their solution in the case s=q^-3/2 using a recursion relation. At the combinatorial point q^1/2= e^-2πi/3 the solution reduces to the ground state of the dense O(1) loop model on a strip with open boundary conditions. We present an alternative construction of such ground state based on the knowledge of the ground state of the same model with mixed boundary conditions and prove that the sum rule as of its components is given by the product of four symplectic characters.

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