On page 14 of Craig Tracy's slides on ASEP, it states that the $n$-particle boundary condition can be reduced to the 2-particle boundary condition due to the fact that the $S$-matrix satisfies the Yang-Baxter equation.

I assume the $S$-matrix is the Yang-Yang $S$-matrix on page 16:

$$S_{\alpha\beta} = - {p + q \xi_\alpha \xi_\beta - \xi_\alpha \over p + q \xi_\alpha \xi_\beta - \xi_\beta}$$

My question is, what is the Yang-Baxter equation written in terms of these $S$-matrices?

I can find on the Internet introductions to the Yang-Baxter equations in the language of quantum spin chains (with relevant examples of XXX and XXZ chains), but I can't spot in them any equations involving the $S$-matrix defined above. Thanks in advance.