The Asymmetric Simple Exclusion Process, a classical particle gas model in 1D with hard-core interactions,
is one of the most studied toy models in nonequilibrium statistical physics, in part due to the fact that it is
integrable, hence solvable in principle.
In this informal talk, I will present techniques that give access to certain key properties of the model, such as
the generating function of the stationary current of particles. These techniques rely on the construction of a
transfer matrix with two spectral parameters starting from basic elements of the Uq(Sl2) algebra, which can
be identified with Baxter's Q-operator, and whose spectrum verifies special q-differential equations that can
be solved perturbatively.
