{"paper":{"title":"Crystal bases of q-deformed Kac modules over the quantum superalgebra $U_q(\\gl(m|n))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Jae-Hoon Kwon","submitted_at":"2012-03-26T07:23:10Z","abstract_excerpt":"We introduce the notion of a crystal base of a finite dimensional q-deformed Kac module over the quantum superalgebra $U_q(\\gl(m|n))$, and prove its existence and uniqueness. In particular, we obtain the crystal base of a finite dimensional irreducible $U_q(\\gl(m|n))$-module with typical highest weight. We also show that the crystal base of a q-deformed Kac module is compatible with that of its irreducible quotient $V(\\lambda)$ given by Benkart, Kang and Kashiwara when $V(\\lambda)$ is an irreducible polynomial representation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5590","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"}