Boundary matrices for the higher spin six vertex model

Vladimir V. Mangazeev, Xilin Lu

Published 2019-03-01Version 1

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 $U_q(\widehat{sl(2)})$. 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.