# Boundary matrices for the higher spin six vertex model

## TL;DR

This paper derives explicit formulas for boundary K-matrices in the higher spin six vertex model, generalizing known cases and providing solutions for arbitrary spin using hypergeometric functions.

## Contribution

It introduces a method to compute boundary K-matrices for any spin in the higher spin six vertex model, expanding beyond known low-spin solutions.

## Key findings

- Explicit formulas for K-matrices for arbitrary spin s.
- Solutions expressed in terms of hypergeometric functions.
- Simplifications occur for triangular K-matrices, reducing to q-Pochhammer symbols.

## 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.