{"paper":{"title":"Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Euiyong Park, Masaki Kashiwara, Seok-Jin Kang","submitted_at":"2012-02-08T08:27:13Z","abstract_excerpt":"We construct a geometric realization of the Khovanov-Lauda-Rouquier algebra $R$ associated with a symmetric Borcherds-Cartan matrix $A=(a_{ij})_{i,j\\in I}$ via quiver varieties. As an application, if $a_{ii} \\ne 0$ for any $i\\in I$, we prove that there exists a 1-1 correspondence between Kashiwara's lower global basis (or Lusztig's canonical basis) of $U_\\A^-(\\g)$ (resp.\\ $V_\\A(\\lambda)$) and the set of isomorphism classes of indecomposable projective graded modules over $R$ (resp.\\ $R^\\lambda$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1622","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"}