On a_2^(1) Reflection Matrices and Affine Toda Theories
  We construct new non-diagonal solutions to the boundary Yang-Baxter-Equation corresponding to a two-dimensional field theory with U_q(a_2^(1)) quantum affine symmetry on a half-line. The requirements of boundary unitarity and boundary crossing symmetry are then used to find overall scalar factors which lead to consistent reflection matrices. Using the boundary bootstrap equations we also compute the reflection factors for scalar bound states (breathers). These breathers are expected to be identified with the fundamental quantum particles in a_2^(1) affine Toda field theory and we therefore obtain a conjecture for the affine Toda reflection factors. We compare these factors with known classical results and discuss their duality properties and their connections with particular boundary conditions. 
Georg M. Gandenberger