Twisted algebra R-matrices and S-matrices for $b_n^{(1)}$ affine Toda solitons and their bound states

Abstract

We construct new $U_q(a^{(2)}_{2n-1})$ and $U_q(e^{(2)}_6)$ invariant $R$-matrices and comment on the general construction of $R$-matrices for twisted algebras. We use the former to construct $S$-matrices for $b^{(1)}_n$ affine Toda solitons and their bound states, identifying the lowest breathers with the $b^{(1)}_n$ particles.