{"paper":{"title":"A generalized Asymmetric Exclusion Process with $U_q(\\mathfrak{sl}_2)$ stochastic duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.QA"],"primary_cat":"math.PR","authors_text":"Cristian Giardina', Frank Redig, Gioia Carinci, Tomohiro Sasamoto","submitted_at":"2014-07-12T10:27:28Z","abstract_excerpt":"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 $q\\in (0,1)$ and where at most $2j\\in\\mathbb{N}$ particles per site are allowed. The process is constructed from a $(2j+1)$-dimensional representation of a quantum Hamiltonian with $U_q(\\mathfrak{sl}_2)$ 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 mak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3367","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}