{"paper":{"title":"Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators. Part II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Justyna Kosakowska, Mariusz Kaniecki, Markus Schmidmeier","submitted_at":"2016-09-28T19:06:36Z","abstract_excerpt":"For a partition $\\beta$, denote by $N_\\beta$ the nilpotent linear operator of Jordan type $\\beta$. Given partitions $\\beta$, $\\gamma$, we investigate the representation space ${}_2{\\mathbb V}_{\\gamma}^\\beta$ of all short exact sequences $$ \\mathcal E: 0\\to N_\\alpha \\to N_\\beta \\to N_\\gamma \\to 0$$ where $\\alpha$ is any partition with each part at most 2. Due to the condition on $\\alpha$, the isomorphism type of a sequence $\\mathcal E$ is given by an arc diagram $\\Delta$; denote by ${\\mathbb V}_\\Delta$ the subset of ${}_2{\\mathbb V}_{\\gamma}^\\beta$ of all sequences isomorphic to $\\mathcal E$.\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09042","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"}