Interacting particle systems with type D symmetry and duality

Abstract

We construct a two-class asymmetric interacting particle system with $U_q(s{o}_6)$ or $U_q(s{o}_8)$ symmetry, in which up to two particles may occupy a site if the two particles have different class. The particles exhibit a drift, but there is no preference given between first-class and second-class particles. The quantum group symmetry leads to reversible measures and a self-duality for the particle system. Additionally, a new method is developed to construct a symmetric interacting particle system from the Casimir element of $s{o}_{2n}$.