Integrable boundary conditions for multi-species ASEP
  The first result of the present paper is to provide classes of explicit solutions for integrable boundary matrices for the multi-species ASEP with an arbitrary number of species.   All the solutions we have obtained can be seen as representations of a new algebra that contains the boundary Hecke algebra. The boundary Hecke algebra is not sufficient to build these solutions. This is the second result of our paper. 
N. Crampe, C. Finn, E. Ragoucy and M. Vanicat
math-ph cond-mat.stat-mech math.MP