{"paper":{"title":"The crossing model for regular $A_n$-crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"A.V.Karzanov, G.A.Koshevoy, V.I.Danilov","submitted_at":"2006-12-13T16:44:35Z","abstract_excerpt":"A regular $A_n$-crystal is an edge-colored directed graph, with $n$ colors, related to an irreducible highest weight integrable module over $U_q(sl_{n+1})$. Based on Stembridge's local axioms for regular simply-laced crystals and a structural characterization of regular $A_2$-crystals in \\cite{DKK-07}, we present a new combinatorial construction, the so-called {\\em crossing model}, and prove that this model generates precisely the set of regular $A_n$-crystals.\n  Using the model, we obtain a series of results on the combinatorial structure of such crystals and properties of their subcrystals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612360","kind":"arxiv","version":2},"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"}