{"paper":{"title":"Rank-one geometry and mixed complexes in representations of Cartan type Lie algebras on a torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"S.Eswara Rao, Souvik Pal","submitted_at":"2025-04-20T07:31:00Z","abstract_excerpt":"In this paper, we develop a unified theory of reducibility and indecomposability for Shen-Larsson modules over the Witt, special and Hamiltonian type Lie algebras on a torus. Our approach is based on a rank-one mechanism governing irreducible submodules, Loewy filtrations, rank reduction, uniseriality and mixed complex structures. We first provide a uniform intrinsic characterization of the trivial and fundamental representations of $gl_N, sl_N, sp_{2n}$ in terms of quadratic relations satisfied by rank-one elements of these matrix Lie algebras and utilize it to determine the irreducibility of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14517","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.14517/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}