2019/03/12 by Vladimir V. Mangazeev, Xilin Lu · 9 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Affine transformation #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Boundary (topology) #Combinatorics #Eigenvalues and eigenvectors #Graph #Hypergeometric function #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix function #Permutation matrix #Physics #Pure mathematics #Quantum affine algebra #Quantum mechanics #Random Matrices and Applications #Spin (aerodynamics) #Spins #Symmetric matrix #Triangular matrix #Vertex (graph theory) #math-ph #math.MP #math.QA #msc:33D15 #msc:81R50 #nlin.SI
paper · pdf · doi:10.1016/j.nuclphysb.2019.114665
published in Nuclear Physics B 945, 114665 (Elsevier BV) · Misprints fixed, acknowledgements added
arxiv created 2019/03/12 · openalex publication_date 2019/06/03 · arxiv updated 2019/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we consider solutions to the reflection equation related to the higher spin stochastic six vertex model. The corresponding higher spin R-matrix is associated with the affine quantum algebra Uq(sl(2)ˆ). The explicit formulas for boundary K-matrices for spins s=1/2,1 are well known. We derive difference equations for the generating function of matrix elements of the K-matrix for any spin s and solve them in terms of hypergeometric functions. As a result we derive the explicit formula for matrix elements of the K-matrix for arbitrary spin. In the lower- and upper- triangular cases, the K-matrix simplifies and reduces to simple products of q-Pochhammer symbols.