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A generalized asymmetric exclusion process with U q ( sl 2 ) stochastic duality

We study a new process, which we call ASEP ( q , j ) , where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by q ∈ ( 0 , 1 ) and where at most 2 j ∈ N particles per site are allowed. The process is constructed from a ( 2 j + 1 ) -dimensional representation of a quantum Hamiltonian with U q ( sl 2 ) invariance by applying a suitable ground-state transformation. After showing basic properties of the process ASEP ( q , j ) , we prove self-duality with several self-duality functions constructed from the symmetries of the quantum Hamiltonian. By making use of the self-duality property we compute the ﬁrst q -exponential moment of the current for step initial conditions (both a shock or a rarefaction fan) as well as when the process is started from a homogeneous product measure.