q--exchangeable Measures and Transformations in Interacting Particle Systems

Jeffrey Kuan

Published 2024-09-19Version 1

This paper provides unified calculations regarding certain measures and transformations in interacting particle systems. More specifically, we provide certain general conditions under which an interacting particle system will have a reversible measure, gauge transformation, or ground state transformation. Additionally, we provide a method to prove that these conditions hold. This method uses certain quantum groups, and in that context the general conditions specialize to a \(q\)--exchangeable property.