A New Dynamical Reflection Algebra and Related Quantum Integrable Systems

We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang–Baxter equations, coactions, fusions, and commuting traces are derived. Explicit examples are given and quantum integrable Hamiltonians are constructed. They exhibit features similar to the Ruijsenaars–Schneider Hamiltonians.