{"paper":{"title":"Dual Perfect Bases and dual perfect graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Byeong Hoon Kahng, Masaki Kashiwara, Seok-Jin Kang, Uhi Rinn Suh","submitted_at":"2014-05-08T07:21:38Z","abstract_excerpt":"We introduce the notion of dual perfect bases and dual perfect graphs. We show that every integrable highest weight module $V_q(\\lambda)$ over a quantum generalized Kac-Moody algebra $U_{q}(\\mathcal{g})$ has a dual perfect basis and its dual perfect graph is isomorphic to the crystal $B(\\lambda)$. We also show that the negative half $U_{q}^{-}(\\mathcal{g})$ has a dual perfect basis whose dual perfect graph is isomorphic to the crystal $B(\\infty)$. More generally, we prove that all the dual perfect graphs of a given dual perfect space are isomorphic as abstract crystals. Finally, we show that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1820","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"}