Boundary matrices for the higher spin six vertex model

Abstract

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.

Misprints fixed, acknowledgements added

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Cited by in corpus (7)

• Non-compact quantum spin chains as integrable stochastic particle processes
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• Random walk on nonnegative integers in beta distributed random environment
• Integrable boundaries for the q-Hahn process
• Generic triangular solutions of the reflection equation: $U_q(\widehat{s{l}_2})$ case
• Reflection $K$ matrices associated with an Onsager coideal of $U_p(A_{n-1}^{(1)})$, $U_p(B_n^{(1)})$, $U_p(D_n^{(1)})$ and $U_p(D_{n+1}^{(2)})$
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$