In this talk I will show how the same algebraic approach, which relies on the su(1,1) Lie algebra, can be used to construct two duality results. One is well-known: the two processes involved are the symmetric inclusion process and a Markov diffusion called Brownian Energy process. The other one is a new result in collaboration with C. Giardinà and R. Frasssek which involves a particle system of zero-range type, called harmonic process, and a redistribution model similar to the Kipnis-Marchioro-Presutti model. For these models all moments in the stationary nonequilibrium state can be explicitly computed and we can characterize the invariant measure as a mixture of inhomogeneous products of exponential distributions.
