We study two generalizations of the asymmetric simple exclusion process (ASEP) with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type 2 can only influence the jump rates of particles of type 1. We prove that the processes are self-dual and explicitly write the duality function. The construction and proofs of duality are accomplished using symmetry of the quantum groups Uq(gl_3) and Uq(sp_4), generalizing the U_q(sl_2) symmetry of ASEP.

Jeffrey Kuan (Columbia)Wed, Feb 10

We study two generalizations of the asymmetric simple exclusion process (ASEP) with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type 2 can only influence the jump rates of particles of type 1. We prove that the processes are self-dual and explicitly write the duality function. The construction and proofs of duality are accomplished using symmetry of the quantum groups Uq(gl_3) and Uq(sp_4), generalizing the U_q(sl_2) symmetry of ASEP.