{"paper":{"title":"Combinatorics of Character Formulas for the Lie Superalgebra $\\fgl(m,n).$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ian M. Musson, Vera V. Serganova","submitted_at":"2011-04-09T03:25:42Z","abstract_excerpt":"Let $\\fg$ be the Lie superalgebra $\\fgl(m,n).$ Algorithms for computing the composition factors and multiplicities of Kac modules for $\\fg$ were given by the second author in 1996, and by J. Brundan in 2003.\n  We give a combinatorial proof of the equivalence between the two algorithms. The proof uses weight and cap diagrams introduced by Brundan and C. Stroppel, and cancelations between paths in a graph $\\mathcal{G}$ defined using these diagrams. Each vertex of $\\mathcal{G}$ corresponds to a highest weight of a finite dimensional simple module, and each edge is weighted by a nonnegative intege"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1668","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"}