This functions checks if the Young Baxter equation holds. In particular, for up and down actions, let there be a switch $S(a,b_a) = (b,a^b)$ and define $S_1(a,b,c)=(S(a,b),c)$ and $S_2(a,b,c)=(a,S(b,c))$. Then the Young Baxter equations are
$$S_1S_2S_1(a,b,c) = S_2S_1S_2(a,b,c)$$