Quantum algebra symmetry of the ASEP with second-class particles

Abstract

We consider a two-component asymmetric simple exclusion process (ASEP) on a finite lattice with reflecting boundary conditions. For this process, which is equivalent to the ASEP with second-class particles, we construct the representation matrices of the quantum algebra $U_q[\mathfrak{gl}(3)]$ that commute with the generator. As a byproduct we prove reversibility and obtain in explicit form the reversible measure. A review of the algebraic techniques used in the proofs is given.

23 pages, presented at conference Particle systems and PDE's - III, 17-19 Dec 2014, Braga, Portugal

References in corpus (3)

• Matrix representation of the stationary measure for the multispecies TASEP
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Self-Duality for the Two-Component Asymmetric Simple Exclusion Process

Cited by in corpus (10)

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• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• Self-duality of Markov processes and intertwining functions
• Uphill in reaction-diffusion multi-species interacting particles systems
• Limiting current distribution for a two species asymmetric exclusion process
• Regularity comparison of symbolic powers, integral closure of powers and powers of edge ideals
• Duality relations for the ASEP conditioned on a low current
• Orthogonal polynomial duality of a two-species asymmetric exclusion process
• The steady state of the boundary-driven multiparticle asymmetric diffusion model