Interacting particle systems with type D symmetry and duality

TL;DR

This paper introduces a novel two-class asymmetric interacting particle system with quantum group symmetry, demonstrating self-duality and reversible measures, and develops a new method to construct symmetric systems from Casimir elements.

Contribution

It constructs a new class of particle systems with specific symmetries and introduces a method to derive symmetric systems from algebraic Casimir elements.

Findings

System exhibits self-duality and reversibility.

Particles can occupy sites with up to two particles of different classes.

Develops a new algebraic method for constructing symmetric particle systems.

Abstract

We construct a two-class asymmetric interacting particle system with $U_q(so_6)$ or $U_q(so_8)$ 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 $so_{2n}$.