Factorizing particles on a half-line and root systems

Factorization conditions are obtained and an example is given of a theory of equal-mass relativistic particles on a half-line with reflection corresponding to the $B_n$, $C_n$, $D_n$ root systems. Generalized factorization equations are introduced, and the analog of Yang's $S$ matrix is considered for an arbitrary root system. For the system $B_n$ an example of an $S$ matrix with elliptic dependence on the rapidities is constructed; it generalizes Belavin's $S$ matrix.