Coxeter Group Actions on Interacting Particle Systems

Understand

We provide a conceptual proof of the color-position symmetry of colored ASEP by relating it to the actions of Coxeter groups.

• The group action (and hence the color-position symmetry) also applies to more general interacting particle systems, such as the colored ASEP(q,j) or systems with open boundary conditions.
• As an application, we find the asymptotics of the expected positions of second-class particles in the ASEP(q,j).