{"paper":{"title":"PBW filtration and bases for symplectic Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Evgeny Feigin, Ghislain Fourier, Peter Littelmann","submitted_at":"2010-10-12T08:06:04Z","abstract_excerpt":"We study the PBW filtration on the highest weight representations $V(\\la)$ of $\\msp_{2n}$. This filtration is induced by the standard degree filtration on $U(\\n^-)$. We give a description of the associated graded $S(\\n^-)$-module $gr V(\\la)$ in terms of generators and relations. We also construct a basis of $gr V(\\la)$. As an application we derive a graded combinatorial formula for the character of $V(\\la)$ and obtain a new class of bases of the modules $V(\\la)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2321","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"}