{"paper":{"title":"On the combinatorial structure of crystals of types A,B,C","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Karzanov, Gleb Koshevoy, Vladimir Danilov","submitted_at":"2012-01-22T11:04:27Z","abstract_excerpt":"Regular $A_n$-, $B_n$- and $C_n$-crystals are edge-colored directed graphs, with ordered colors $1,2,...,n$, which are related to representations of quantized algebras $U_q(\\mathfrak{sl}_{n+1})$, $U_q(\\mathfrak{sp}_{2n})$ and $U_q(\\mathfrak{so}_{2n+1})$, respectively. We develop combinatorial methods to reveal refined structural properties of such objects.\n  Firstly, we study subcrystals of a regular $A_n$-crystal $K$ and characterize pairwise intersections of maximal subcrystals with colors $1,...,n-1$ and colors $2,...,n$. This leads to a recursive description of the structure of $K$ and pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4549","kind":"arxiv","version":3},"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"}