{"paper":{"title":"Homology of Littlewood complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.RT","authors_text":"Andrew Snowden, Jerzy Weyman, Steven V Sam","submitted_at":"2012-09-16T18:23:46Z","abstract_excerpt":"Let V be a symplectic vector space of dimension 2n. Given a partition \\lambda with at most n parts, there is an associated irreducible representation S_{[\\lambda]}(V) of Sp(V). This representation admits a resolution by a natural complex L^\\lambda, which we call the Littlewood complex, whose terms are restrictions of representations of GL(V). When \\lambda has more than n parts, the representation S_{[\\lambda]}(V) is not defined, but the Littlewood complex L^\\lambda still makes sense. The purpose of this paper is to compute its homology. We find that either L^\\lambda is acyclic or that it has a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3509","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"}