Laurent polynomial solutions of the boundary quantum\n Knizhnik--Zamolodchikov equation

2014/12/25 by Keiichi Shigechi, Shigechi, Keiichi
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Boundary (topology) #Boundary value problem #Computer science #Construct (python library) #Degree (music) #FOS: Mathematics #FOS: Physical sciences #Laurent polynomial #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Physics #Polynomial #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum mechanics #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.1412.7797

22 pages

arxiv created 2014/12/25 · openalex publication_date 2014/12/25 · arxiv updated 2014/12/30 · openalex created_date 2022/09/03 · openalex updated_date 2026/08/05

Abstract

We construct Laurent polynomial solutions of the boundary quantum\nKnizhnik--Zamolodchikov equation for U_q( widehat mathfraksl₂) on\nthe parabolic Kazhdan--Lusztig bases. They are characterized by non-symmetric\nKoornwinder polynomials with the specialized parameters. As a special case, we\nobtain the solution of the minimal degree.\n

Citations

• Determinat formula for solutions of the U_q(sl_n) qKZ equation at |q|=1
• Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation
• Kazhdan-Lusztig polynomials for the Hermitian symmetric pair (B_N,A_N-1)
• The two-boundary Temperley–Lieb algebra
• Boundary conditions for integrable quantum systems
• A Positive integral property on the ground state of the two-boundary Temperley--Lieb Hamiltonian
• Zeros of Symmetric Laurent Polynomials of Type (BC)_n and Koornwinder-Macdonald Polynomials Specialized at t^k+1q^r-1=1

Related

• Quantum Knizhnik-Zamolodchikov Equation, Totally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices
• The integral formula for the solutions of the quantum Knizhnik-Zamolodchikov equation associated with U_q(sl_n) for |q|=1
• On solutions of the KZ and qKZ equations at level zero
• The quantum Knizhnik-Zamolodchikov equation and non-symmetric Macdonald polynomials
• Theta function solutions of the qKZB equation for a face model